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Relevant bibliographies by topics / Real characteristic classes of complex vector bundles

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Academic literature on the topic 'Real characteristic classes of complex vector bundles'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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Journal articles on the topic "Real characteristic classes of complex vector bundles"

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YANG, HUIJUN. "A REMARK ON THE STABLE REAL FORMS OF COMPLEX VECTOR BUNDLES OVER MANIFOLDS." Bulletin of the Australian Mathematical Society 96, no. 1 (2017): 69–76. http://dx.doi.org/10.1017/s0004972717000132.

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Let$M$be an$n$-dimensional closed oriented smooth manifold with$n\equiv 4\;\text{mod}\;8$, and$\unicode[STIX]{x1D702}$be a complex vector bundle over$M$. We determine the final obstruction for$\unicode[STIX]{x1D702}$to admit a stable real form in terms of the characteristic classes of$M$and$\unicode[STIX]{x1D702}$. As an application, we obtain the criteria to determine which complex vector bundles over a simply connected four-dimensional manifold admit a stable real form.

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Krasnov, Vyacheslav A. "CHARACTERISTIC CLASSES OF VECTOR BUNDLES ON A REAL ALGEBRAIC VARIETY." Mathematics of the USSR-Izvestiya 39, no. 1 (1992): 703–30. http://dx.doi.org/10.1070/im1992v039n01abeh002223.

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Haibao, Duan. "Characteristic classes for complex bundles with trivial real reduction." Proceedings of the American Mathematical Society 128, no. 8 (2000): 2465–71. http://dx.doi.org/10.1090/s0002-9939-00-05734-8.

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Moutuou, El-Kaïoum M. "Equivariant KK-theory for generalised actions and Thom isomorphism in groupoid twisted K-theory." Journal of K-Theory 13, no. 1 (2013): 83–113. http://dx.doi.org/10.1017/is013010018jkt244.

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AbstractWe develop equivariant KK–theory for locally compact groupoid actions by Morita equivalences on real and complex graded C*-algebras. Functoriality with respect to generalised morphisms and Bott periodicity are discussed. We introduce Stiefel-Whitney classes for real or complex equivariant vector bundles over locally compact groupoids to establish the Thom isomorphism theorem in twisted groupoid K–theory.

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Bochnak, J., and W. Kucharz. "K-theory of real algebraic surfaces and threefolds." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 3 (1989): 471–80. http://dx.doi.org/10.1017/s0305004100068213.

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LetXbe an affine real algebraic variety, i.e., up to biregular isomorphism an algebraic subset of ℝn. (For definitions and notions of real algebraic geometry we refer the reader to the book [6].) Letdenote the ring of regular functions onX([6], chapter 3). (IfXis an algebraic subset of ℝnthenis comprised of all functions of the formf/g, whereg, f: X→ ℝ are polynomial functions withg−1(O) = Ø.) In this paper, assuming thatXis compact, non-singular, and that dimX≤ 3, we compute the Grothendieck groupof projective modules over(cf. Section 1), and the Grothendieck groupand the Witt groupof symplec

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Guillot, Pierre, and Ján Mináč. "Milnor K-theory and the graded representation ring." Journal of K-theory 13, no. 3 (2014): 447–80. http://dx.doi.org/10.1017/is014004004jkt261.

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AbstractLet F be a field, let G = Gal(/F) be its absolute Galois group, and let R(G,k) be the representation ring of G over a suitable field k. In this preprint we construct a ring homomorphism from the mod 2 Milnor K-theory k*(F) to the graded ring grR(G,k) associated to Grothendieck's γ-filtration. We study this map in particular cases, as well as a related map involving the W-group of F, rather than G. The latter is an isomorphism in all cases considered.Naturally this echoes the Milnor conjecture (now a theorem), which states that k*(F) is isomorphic to the mod 2 cohomology of the absolute

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Naolekar, Aniruddha, and Ajay Thakur. "Note on the characteristic rank of vector bundles." Mathematica Slovaca 64, no. 6 (2014). http://dx.doi.org/10.2478/s12175-014-0289-4.

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AbstractWe define the notion of characteristic rank, charrankX(ξ), of a real vector bundle ξ over a connected finite CW-complex X. This is a bundle-dependent version of the notion of characteristic rank introduced by Július Korbaš in 2010. We obtain bounds for the cup length of manifolds in terms of the characteristic rank of vector bundles generalizing a theorem of Korbaš and compute the characteristic rank of vector bundles over the Dold manifolds, the Moore spaces and the stunted projective spaces amongst others.

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Dissertations / Theses on the topic "Real characteristic classes of complex vector bundles"

1

Rahm, Alexander. "Characteristic classes of vector bundles with extra structure." Thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-000D-F285-2.

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