Academic literature on the topic 'Bundle gerbes'

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Journal articles on the topic "Bundle gerbes"

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SZAMOTULSKI, MARCIN, and DOROTA MARCINIAK. "TOTAL SPACE OF ABELIAN GERBES." International Journal of Modern Physics A 24, no. 15 (2009): 2877–88. http://dx.doi.org/10.1142/s0217751x09046229.

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We present a generalization of the construction of a principal G-bundle from a one Čech cocycle to the case of higher abelian gerbes. We prove that the sheaf of local sections of the associated bundle to a higher abelian gerbe is isomorphic to the sheaf of sections of the gerbe itself. Our main result states that equivalence classes of higher abelian gerbes are in bijection with isomorphism classes of the corresponding bundles. We also present topological characterization of those bundles. In the last section, we show that the usual notion of Ehresmann connection leads to the gerbe connection
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JURČO, BRANISLAV. "CROSSED MODULE BUNDLE GERBES; CLASSIFICATION, STRING GROUP AND DIFFERENTIAL GEOMETRY." International Journal of Geometric Methods in Modern Physics 08, no. 05 (2011): 1079–95. http://dx.doi.org/10.1142/s0219887811005555.

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We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to a (Lie) crossed module (H → D) there is a simplicial group [Formula: see text], the nerve of the groupoid [Formula: see text] defined by the crossed module, and its geometric realization, the topological group [Formula: see text]. We introduce crossed module bundle gerbes so that their (stable) equivalence classes are in a bijection with equivalence classes of principal [Formula: see text]-bundles. We discuss the string group and string structures from this point of view. Also, we give a
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Bunk, Severin. "Gerbes in Geometry, Field Theory, and Quantisation." Complex Manifolds 8, no. 1 (2021): 150–82. http://dx.doi.org/10.1515/coma-2020-0112.

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Abstract This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain the classification of bundle gerbes with connection in terms of differential cohomology. We then survey how the surface holonomy of bundle gerbes combines with their transgression line bundles to yield a smooth bordism-type field theory. Finally, we exhibit the use of bundle gerbes in geometric quantisation of 2-plectic as well as 1- and 2-shifted s
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Murray, M. K. "Bundle Gerbes." Journal of the London Mathematical Society 54, no. 2 (1996): 403–16. http://dx.doi.org/10.1112/jlms/54.2.403.

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JURČO, BRANISLAV. "NONABELIAN BUNDLE 2-GERBES." International Journal of Geometric Methods in Modern Physics 08, no. 01 (2011): 49–78. http://dx.doi.org/10.1142/s0219887811004963.

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We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. If (L → M → N) is a Lie 2-crossed module and Y → X is a surjective submersion then an (L → M → N)-bundle 2-gerbe over X is defined in terms of a so-called (L → M → N)-bundle gerbe over the fiber product Y[2] = Y × XY, which is an (L → M)-bundle gerbe over Y[2] equipped with a trivialization under the change of its structure crossed module from L → M to 1 → N, and which is subjected to further conditions on higher fiber products Y[3], Y[4] and Y[5]. String structures can be describe
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Stevenson, Daniel. "Bundle 2-Gerbes." Proceedings of the London Mathematical Society 88, no. 02 (2004): 405–35. http://dx.doi.org/10.1112/s0024611503014357.

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Murray, Michael K., David Michael Roberts, Danny Stevenson, and Raymond F. Vozzo. "Equivariant bundle gerbes." Advances in Theoretical and Mathematical Physics 21, no. 4 (2017): 921–75. http://dx.doi.org/10.4310/atmp.2017.v21.n4.a3.

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Bunk, Severin, Christian Sämann, and Richard J. Szabo. "The 2-Hilbert space of a prequantum bundle gerbe." Reviews in Mathematical Physics 30, no. 01 (2018): 1850001. http://dx.doi.org/10.1142/s0129055x18500010.

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We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier–Douady class is torsion. Analogously to usual prequantization, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf’s version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbe
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Bunk, Severin, Lukas Müller, and Richard J. Szabo. "Smooth 2-Group Extensions and Symmetries of Bundle Gerbes." Communications in Mathematical Physics 384, no. 3 (2021): 1829–911. http://dx.doi.org/10.1007/s00220-021-04099-7.

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AbstractWe study bundle gerbes on manifolds M that carry an action of a connected Lie group G. We show that these data give rise to a smooth 2-group extension of G by the smooth 2-group of hermitean line bundles on M. This 2-group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-group extension in terms of a homotopy-coherent version of
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MURRAY, MICHAEL K., and RAYMOND F. VOZZO. "CIRCLE ACTIONS, CENTRAL EXTENSIONS AND STRING STRUCTURES." International Journal of Geometric Methods in Modern Physics 07, no. 06 (2010): 1065–92. http://dx.doi.org/10.1142/s0219887810004725.

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The caloron correspondence can be understood as an equivalence of categories between G-bundles over circle bundles and LG ⋊ρ S1-bundles where LG is the group of smooth loops in G. We use it, and lifting bundle gerbes, to derive an explicit differential form based formula for the (real) string class of an LG ⋊ρ S1-bundle.
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Dissertations / Theses on the topic "Bundle gerbes"

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Stevenson, Daniel. "The geometry of bundle gerbes." Title page, abstract and contents only, 2000. http://web4.library.adelaide.edu.au/theses/09PH/09phs847.pdf.

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Bibliography: p. 141-143 This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2-gerbe. The notion of a bundle 2-gerbe connection and 2-curving are introduced and it is shown that there is a class in H4(M;Z) associated to any bundle 2-gerbe. (Abstract)
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Bunk, Severin. "Categorical structures on bundle gerbes and higher geometric prequantisation." Thesis, Heriot-Watt University, 2017. http://hdl.handle.net/10399/3344.

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We present a construction of a 2-Hilbert space of sections of a bundle gerbe, a suitable candidate for a prequantum 2-Hilbert space in higher geometric quantisation. We start by briefly recalling the construction of the 2-category of bundle gerbes, with minor alterations that allow us to endow morphisms with additive structures. The morphisms in the resulting 2-categories are investigated in detail. We introduce a direct sum on morphism categories of bundle gerbes and show that these categories are cartesian monoidal and abelian. Endomorphisms of the trivial bundle gerbe, or higher functions,
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Mertsch, Darvin Verfasser], Konrad [Akademischer Betreuer] [Waldorf, Konrad Gutachter] Waldorf, Thomas [Gutachter] Schick, and Eckhard [Gutachter] [Meinrenken. "Geometric Models of Twisted K-Theory based Bundle Gerbes and Algebra Bundles / Darvin Mertsch ; Gutachter: Konrad Waldorf, Thomas Schick, Eckhard Meinrenken ; Betreuer: Konrad Waldorf." Greifswald : Universität Greifswald, 2020. http://nbn-resolving.de/urn:nbn:de:gbv:9-opus-40972.

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Mertsch, Darvin [Verfasser], Konrad [Akademischer Betreuer] Waldorf, Konrad [Gutachter] Waldorf, Thomas [Gutachter] Schick, and Eckhard [Gutachter] Meinrenken. "Geometric Models of Twisted K-Theory based Bundle Gerbes and Algebra Bundles / Darvin Mertsch ; Gutachter: Konrad Waldorf, Thomas Schick, Eckhard Meinrenken ; Betreuer: Konrad Waldorf." Greifswald : Universität Greifswald, 2020. http://d-nb.info/1222161834/34.

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Demircioglu, Aydin. "Reconstruction of deligne classes and cocycles." Phd thesis, Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2007/1375/.

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In der vorliegenden Arbeit verallgemeinern wir im Wesentlichen zwei Theoreme von Mackaay-Picken und Picken (2002, 2004). Im ihrem Artikel zeigen Mackaay und Picken,dass es eine bijektive Korrespodenz zwischen Deligne 2-Klassen $xi in check{H}^2(M, mathcal{D}^2)$ und Holonomie Abbildungen von der zweiten dünnen Homotopiegruppe $pi_2^2(M)$ in die abelsche Gruppe $U(1)$ gibt. Im zweiten Artikel wird eine Verallgemeinerung dieses Theorems bewiesen: Picken zeigt, dass es eine Bijektion gibt zwischen Deligne 2-Kozykeln und gewissen 2-dimensionalen topologischen Quantenfeldtheorien. In dieser Arbei
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Gergen, Thomas [Verfasser]. "Die Nachdruckprivilegienpraxis Württembergs im 19. Jahrhundert und ihre Bedeutung für das Urheberrecht im Deutschen Bund. / Thomas Gergen." Berlin : Duncker & Humblot, 2010. http://d-nb.info/1238357385/34.

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Becker, Kimberly Elise. "Bundle gerbes and the Weyl map." Thesis, 2019. http://hdl.handle.net/2440/121598.

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This thesis reviews bundle gerbe theory and the well-known basic bundle gerbe over SU(n). We introduce the cup product bundle gerbe, and show it is stably isomorphic to the pullback of the basic bundle gerbe by the Weyl map. This result enriches our understanding of the basic bundle gerbe, which has numerous applications in physics.<br>Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 2019
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Johnson, Stuart (Stuart James). "Constructions with bundle gerbes / Stuart Johnson." 2002. http://hdl.handle.net/2440/21885.

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"19 July 2002."<br>Bibliography: leaves 135-137.<br>viii, 137 leaves : ill. ; 30 cm.<br>Title page, contents and abstract only. The complete thesis in print form is available from the University Library.<br>This thesis develops the theory of bundle gerbes and examines and number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead to some interesting applications in physics.<br>Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 2003
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Johnson, Stuart (Stuart James). "Constructions with bundle gerbes / Stuart Johnson." Thesis, 2002. http://hdl.handle.net/2440/21885.

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"19 July 2002."<br>Bibliography: leaves 135-137.<br>viii, 137 leaves : ill. ; 30 cm.<br>This thesis develops the theory of bundle gerbes and examines and number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead to some interesting applications in physics.<br>Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 2003
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Stevenson, Daniel. "The geometry of bundle gerbes / Daniel Stevenson." Thesis, 2000. http://hdl.handle.net/2440/19605.

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Bibliography: p. 141-143<br>viii, 143 p. ; 30 cm.<br>This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2-gerbe. The notion of a bundle 2-gerbe connection and 2-curving are introduced and it is shown that there is a class in H4(M;Z) associated to any bundle 2-gerbe. (Abstract)<br>Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 2000
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Books on the topic "Bundle gerbes"

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Huybrechts, D. Fourier-Mukai Transforms in Algebraic Geometry. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.001.0001.

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This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of
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Book chapters on the topic "Bundle gerbes"

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Murray, Michael K. "An Introduction to Bundle Gerbes." In The Many Facets of Geometry. Oxford University Press, 2010. http://dx.doi.org/10.1093/acprof:oso/9780199534920.003.0012.

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Picken, Roger. "A Cohomological Description of Abelian Bundles and Gerbes." In Twenty Years of Bialowieza: A Mathematical Anthology. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701244_0010.

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Abate, Marco. "Index theorems for meromorphic self-maps of the projective space." In Frontiers in Complex Dynamics, edited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691159294.003.0017.

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This chapter uses techniques from the theory of local dynamics of holomorphic germs tangent to the identity to prove three index theorems for global meromorphic maps of projective space. More precisely, the chapter seeks to prove a particular index theorem: Let f : ℙⁿ ⇢ ℙⁿ be a meromorphic self-map of degree ν‎ + 1 ≥ 2 of the complex n-dimensional projective space. Let Σ‎(f) = Fix(f) ∪ I(f) be the union of the indeterminacy set I(f) of f and the fixed points set Fix(f) of f. Let Σ‎(f) = ⊔subscript Greek Small Letter AlphaΣ‎subscript Greek Small Letter Alpha be the decomposition of Σ‎ in connected components, and denote by N the tautological line bundle of ℙⁿ. After laying out the statements under this theorem, the chapter discusses the proofs.
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Verlinden, Claire. "Ambitie en autonomie. Beroepsethiek en een professioneel statuut van leraren." In Code en karakter. Uitgeverij SWP, 2009. http://dx.doi.org/10.36254/978-90-8850-032-9.06.

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In dit artikel wil ik nagaan welke samenhang er bestaat tussen het streven naar een professioneel statuut voor leraren door de Algemene Onderwijs- bond (AOb) en de beroepsethiek van professionals.1 Allereerst wordt ingegaan op de vraag, hoe de AOb tot het idee van een- professioneel statuut is gekomen en hoe vervolgens verschillende actoren in het onderwijsveld en uiteindelijk de minister op dit idee hebben gere- ageerd. De reacties zijn in 2008 geculmineerd in een convenant tussen de minister, de werkgeversorganisaties en onderwijsvakbonden over verbete- ring van de positie van leraren. In dit convenant is vastgelegd dat het be- grip ‘professionele ruimte’ in de onderwijswetgeving zou moeten worden gewaarborgd. Tot slot wordt ingegaan op de vraag waarom het vastleggen van de positie van leraren en de professionele ruimte in een professioneel statuut, alles te maken heeft met beroepsethiek en het thema van deze bundel ‘code en karakter’.
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Yiğit, Faruk. "ROKETSAN’ın Geçmişten Bugüne Olan Teknoloji Yolculuğu ve Türkiye’nin Geleceğindeki Yeri." In Millî Teknoloji Hamlesi: Toplumsal Yansımaları ve Türkiye’nin Geleceği. Türkiye Bilimler Akademisi Yayınları, 2022. http://dx.doi.org/10.53478/tuba.978-625-8352-16-0.ch24.

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Günümüzde küreselleşmenin sonucunda ortaya çıkan ülkeler arasındaki ticaret savaşları ve teknolojik çekişmeler artık dünyadaki dengelerin belirlenmesinde anahtar rol oynamaktadır. Ülkemizin teknolojik ve ekonomik bağımsızlığını sağlama ve küresel güç olma vizyonuyla başlatılan Milli Teknoloji Hamlesi içinde Roketsan’ın yerini ve farklı boyutlardaki gerek doğrudan gerekse de dolaylı katkılarını anlayabilmek için öncelikle şirketin tarihini ve gelişim sürecini bilmek gereklidir. Cumhuriyetin ilk yıllarında Türkiye’de bir teknoloji ve sanayi hamlesi başlamış ancak sürdürebilir olamamıştır. İlerleyen yıllarda dışa olan teknolojik bağımlık artmış ve bunun olumsuz etkileri 1960 ve 1970’lerde Kıbrıs’ta yaşanan sorunlarda açıkça görülmüştür. Kıbrıs Barış Harekâtının ardından bağımsız ve milli bir savunma sanayi kurmaya yönelik gerekli kararlar alınmıştır. Ülkemizin roket ve füze ihtiyaçlarını karşılamak üzere 1988 yılında kurulan Roketsan da bu kararların önemli meyvelerinden birisidir. Teknoloji yarışına çok daha önce başlamış olan rakiplere yetişilmesi ve uluslararası kısıtlarla kontrol edilen roket ve füze teknolojilerinin millileştirilmesi ve bunun yanında yenilikçi teknolojiler geliştirilmesi anlayışı Roketsan’ın ilk başlardan itibaren kurumsal genlerinin önemli bir parçası haline getirilmiştir. 2000’li yılların başında ülkemizin teknolojik ve ekonomik bağımsızlığı için başlatılan Millî Teknoloji Hamlesi ışığında Roketsan’ın gelişim yolculuğu da hız kazanmış ve gerek teknolojik altyapıya ve bilgi birikimine gerekse de nitelikli insan kaynaklarına yapılan bu yatırımlar sonucunda yenilikçi teknolojiler ve başarılı ürünler ortaya konulmuştur. Küreselleşmenin etkisiyle ülkelerin birbiriyle birçok boyutta bağlı hale gelmesi dünyada büyük bir değişim ve dönüşüm sürecini başlatmıştır. Ancak Covid-19 pandemisiyle tetiklenen ekonomik çalkantı ve ülkeler arası ticaret savaşları dünyanın yeni bir döneme girmekte olduğunu işaret etmektedir. Özellikle doğal kaynaklardaki dar boğazlar, küresel ısınmanın daha belirgin hale gelmesiyle beraber hidrokarbon bazlı enerji kaynaklarına alternatif arayışları ve kullanım stratejilerindeki değişim, su ve gıda kaynaklarına erişim riskleri ve bunların yanında mikroelektronik sanayi gibi endüstrilerde kullanılan kritik ham malzeme kaynaklarındaki daralma veya tekelleşme küresel çerçevede gerilimlere, çatışmalara ve hatta savaşlara yol açabilecektir. Bundan sonraki dönemde söz konusu risklerin gerçekleşmesi durumunda ortaya çıkabilecek etkilere hazır olmak, süreci etkin bir şekilde yönetebilmek için Türkiye’nin tüm kurumlarıyla beraber gerekli stratejileri oluşturması ve refleksleri geliştirmesi gerekmektedir. Ülkemizin geleceğinin güvenliği açısından son derece kritik önem taşıyan Roketsan bir yandan geleceğin teknolojilerine ve sistemlerine yönelik çalışmalarını sürdürmekte diğer yandan beklenmedik krizlere ve olaylara karşı dayanıklılığını artıracak esnek ve uyum sağlayabilen kurumsal süreçler ve sistematik refleksler geliştirmektedir. Roketsan’ın ortaya koyduğu bu strateji ve faaliyetlerin ülkemizin teknoloji hamlesi içinde gerek askeri gerekse de sivil anlamda kritik önem arz ettiği, birçok sektöre büyük faydaları olacağı ve bunun ötesinde toplumumuzun özgüvenini ve teknolojik bilincini artırarak sosyal anlamda da katkı sağlayacağı değerlendirilmektedir.
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Conference papers on the topic "Bundle gerbes"

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LÉANDRE, RÉMI. "BUNDLE GERBES AND BROWNIAN MOTION." In Proceedings of the Fifth International Workshop. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702562_0022.

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TOMODA, ATSUSHI. "A RELATION ON SPIN BUNDLE GERBES AND MAYER'S DIRAC OPERATORS." In Proceedings of the COE International Workshop. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812775061_0021.

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