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1

Brzeziński, Tomasz y Piotr M. Hajac. "The Chern–Galois character". Comptes Rendus Mathematique 338, n.º 2 (enero de 2004): 113–16. http://dx.doi.org/10.1016/j.crma.2003.11.009.

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2

RAMADOSS, AJAY C. "THE BIG CHERN CLASSES AND THE CHERN CHARACTER". International Journal of Mathematics 19, n.º 06 (julio de 2008): 699–746. http://dx.doi.org/10.1142/s0129167x08004856.

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Let X be a smooth scheme over a field of characteristic 0. The Atiyah class of the tangent bundle TX of X equips TX[-1] with the structure of a Lie algebra object in the derived category D +(X) of bounded below complexes of [Formula: see text] modules with coherent cohomology [6]. We lift this structure to that of a Lie algebra object [Formula: see text] in the category of bounded below complexes of [Formula: see text] modules in Theorem 2. The "almost free" Lie algebra [Formula: see text] is equipped with Hochschild coboundary. There is a symmetrization map [Formula: see text] where [Formula: see text] is the complex of polydifferential operators with Hochschild coboundary. We prove a theorem (Theorem 1) that measures how I fails to commute with multiplication. Further, we show that [Formula: see text] is the universal enveloping algebra of [Formula: see text] in D +(X). This is used to interpret the Chern character of a vector bundle E on X as the "character of a representation" (Theorem 4). Theorems 4 and 1 are then exploited to give a formula for the big Chern classes in terms of the components of the Chern character.
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3

Yu, Xuan. "Chern character for matrix factorizations via Chern–Weil". Journal of Algebra 424 (febrero de 2015): 416–47. http://dx.doi.org/10.1016/j.jalgebra.2014.09.024.

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4

Berthomieu, Alain. "A version of smooth K-theory adapted to the total Chern class". Journal of K-Theory 6, n.º 2 (octubre de 2010): 197–230. http://dx.doi.org/10.1017/is010009026jkt104.

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AbstractA new model of smooth K0-theory ([5] [1]) is constructed, with the help of the total Chern class (contrary to the theories considered in ]1], [5], [12] and [13] which use the Chern character). The correspondence with the earlier model [1] is obtained by adapting, at the level of transgression forms, the usual formulae which express the Chern character in terms of the Chern classes and vice versa.The advantage of this new model is that it allows constructing Chern classes with values in integral Chern-Simons characters in a natural way: this construction answers a question asked by U. Bunke [4].
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5

Wang, Xiaolu. "A Bivariant Chern Character, II". Canadian Journal of Mathematics 44, n.º 2 (1 de abril de 1992): 400–435. http://dx.doi.org/10.4153/cjm-1992-027-3.

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In [Con2] Connes introduced cyclic cohomology HC*(A) for an associative algebra A. When A is a complex algebra he constructed a Chern character for p-summable Fredholm modules over A taking values in HC*(A). As a very special case, when X is a closed C∞-manifold and A = C∞ (X), this construction recovers the usual Chern character, which is a rational isomorphism from the K-homology K0(X) to , the even dimensional deRham homology of X.
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6

林, 奕武. "Orbifold Bundle and Chern Character". Pure Mathematics 09, n.º 05 (2019): 627–31. http://dx.doi.org/10.12677/pm.2019.95083.

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7

Gillet, H. y C. Soulé. "On the arithmetic Chern character". Annales de la faculté des sciences de Toulouse Mathématiques 23, n.º 3 (2014): 611–19. http://dx.doi.org/10.5802/afst.1418.

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8

Nistor, Victor. "A Bivariant Chern--Connes Character". Annals of Mathematics 138, n.º 3 (noviembre de 1993): 555. http://dx.doi.org/10.2307/2946556.

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9

Quillen, D. "Superconnections and the Chern character". Topology 24, n.º 2 (1985): 89–95. http://dx.doi.org/10.1016/0040-9383(85)90028-x.

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10

Quillen, Daniel. "Superconnections and the Chern character". Topology 24, n.º 1 (1985): 89–95. http://dx.doi.org/10.1016/0040-9383(85)90047-3.

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11

Bismut, J. M. "Bott-Chern currents, excess normal bundles and the Chern character". Geometric and Functional Analysis 2, n.º 3 (septiembre de 1992): 285–340. http://dx.doi.org/10.1007/bf01896875.

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12

Torii, Takeshi. "HKR characters, $p$-divisible groups and the generalized Chern character". Transactions of the American Mathematical Society 362, n.º 11 (1 de noviembre de 2010): 6159. http://dx.doi.org/10.1090/s0002-9947-2010-05194-3.

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13

Hoyois, Marc, Pavel Safronov, Sarah Scherotzke y Nicolò Sibilla. "The categorified Grothendieck–Riemann–Roch theorem". Compositio Mathematica 157, n.º 1 (enero de 2021): 154–214. http://dx.doi.org/10.1112/s0010437x20007642.

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In this paper we prove a categorification of the Grothendieck–Riemann–Roch theorem. Our result implies in particular a Grothendieck–Riemann–Roch theorem for Toën and Vezzosi's secondary Chern character. As a main application, we establish a comparison between the Toën–Vezzosi Chern character and the classical Chern character, and show that the categorified Chern character recovers the classical de Rham realization.
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14

Zamboni, Luca Quardo. "A Chern character in cyclic homology". Transactions of the American Mathematical Society 331, n.º 1 (1 de enero de 1992): 157–63. http://dx.doi.org/10.1090/s0002-9947-1992-1044967-x.

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15

Perrot, Denis. "Retraction of the Bivariant Chern Character". K-Theory 31, n.º 3 (marzo de 2004): 233–87. http://dx.doi.org/10.1023/b:kthe.0000028983.99109.c9.

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16

Perrot, Denis. "Quasihomomorphisms and the residue Chern character". Journal of Geometry and Physics 60, n.º 10 (octubre de 2010): 1441–73. http://dx.doi.org/10.1016/j.geomphys.2010.05.005.

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17

Gorokhovsky, Alexander. "Bivariant Chern character and longitudinal index". Journal of Functional Analysis 237, n.º 1 (agosto de 2006): 105–34. http://dx.doi.org/10.1016/j.jfa.2006.01.004.

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18

Voigt, Christian. "Chern character for totally disconnected groups". Mathematische Annalen 343, n.º 3 (11 de septiembre de 2008): 507–40. http://dx.doi.org/10.1007/s00208-008-0281-9.

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19

LÜCK, WOLFGANG. "EQUIVARIANT COHOMOLOGICAL CHERN CHARACTERS". International Journal of Algebra and Computation 15, n.º 05n06 (octubre de 2005): 1025–52. http://dx.doi.org/10.1142/s0218196705002773.

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We construct for an equivariant cohomology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients of the equivariant cohomology theory possess a Mackey structure. Such a structure is present in many interesting examples.
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20

Marian, Alina, Dragos Oprea, Rahul Pandharipande, Aaron Pixton y Dimitri Zvonkine. "The Chern character of the Verlinde bundle over ℳ¯ g,n". Journal für die reine und angewandte Mathematik (Crelles Journal) 2017, n.º 732 (1 de noviembre de 2017): 147–63. http://dx.doi.org/10.1515/crelle-2015-0003.

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Abstract We prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over \overline{\mathcal{M}}_{g,n} in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the ranks, given by the Verlinde formula, determine a semisimple fusion algebra). According to Teleman’s classification of semisimple CohFTs, there exists an element of Givental’s group transforming the fusion algebra into the CohFT. We determine the element using the first Chern class of the Verlinde bundle on the interior {\mathcal{M}}_{g,n} and the projective flatness of the Hitchin connection.
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21

Tamme, Georg. "Karoubi’s relative Chern character and Beilinson’s regulator". Annales scientifiques de l'École normale supérieure 45, n.º 4 (2012): 601–36. http://dx.doi.org/10.24033/asens.2174.

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22

Lin, Dexie. "Relative Chern character number and super-connection". Topology and its Applications 234 (febrero de 2018): 155–65. http://dx.doi.org/10.1016/j.topol.2017.11.035.

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23

Stoffel, Augusto. "Dimensional reduction and the equivariant Chern character". Algebraic & Geometric Topology 19, n.º 1 (6 de febrero de 2019): 109–50. http://dx.doi.org/10.2140/agt.2019.19.109.

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24

Rempała, Jan A. "On the Chern character of glued bundles". Annales Polonici Mathematici 48, n.º 2 (1988): 139–52. http://dx.doi.org/10.4064/ap-48-2-139-152.

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25

Xiang, TANG, YAO YiJun y WILLETT Rufus. "Coarse groupoid cohomology and Connes-Chern character". SCIENTIA SINICA Mathematica 47, n.º 12 (28 de noviembre de 2017): 1879–90. http://dx.doi.org/10.1360/n012017-00123.

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26

Wood, Jay A. "The Chern character for classical matrix groups". Proceedings of the American Mathematical Society 126, n.º 4 (1998): 1237–44. http://dx.doi.org/10.1090/s0002-9939-98-04316-0.

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27

Maakestad, Helge. "The Chern character for Lie-Rinehart algebras". Annales de l’institut Fourier 55, n.º 7 (2005): 2551–74. http://dx.doi.org/10.5802/aif.2170.

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28

Torii, Takeshi. "Milnor operations and the generalized Chern character". Geometry and Topology Monographs 10 (18 de abril de 2007): 383–421. http://dx.doi.org/10.2140/gtm.2007.10.383.

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29

Baum, P. y P. Schneider. "Equivariant–Bivariant Chern Character for Profinite Groups". K-Theory 25, n.º 4 (abril de 2002): 313–53. http://dx.doi.org/10.1023/a:1016036724442.

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30

ALBIN, PIERRE y RICHARD MELROSE. "RELATIVE CHERN CHARACTER, BOUNDARIES AND INDEX FORMULAS". Journal of Topology and Analysis 01, n.º 03 (septiembre de 2009): 207–50. http://dx.doi.org/10.1142/s1793525309000151.

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For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have "geometric K-theory", namely the "transmission algebra" introduced by Boutet de Monvel [5], the "zero algebra" introduced by Mazzeo in [9, 10] and the "scattering algebra" from [16], we give explicit formulas for the Chern character of the index bundle in terms of the symbols (including normal operators at the boundary) of a Fredholm family of fiber operators. This involves appropriate descriptions, in each case, of the cohomology with compact supports in the interior of the total space of a vector bundle over a manifold with boundary in which the Chern character, mapping from the corresponding realization of K-theory, naturally takes values.
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31

Klimek, Slawomir y Andrzej Lesniewski. "Chern character in equivariant entire cyclic cohomology". K-Theory 4, n.º 3 (mayo de 1991): 219–26. http://dx.doi.org/10.1007/bf00569447.

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32

Jarvis, Tyler J., Ralph Kaufmann y Takashi Kimura. "Stringy K-theory and the Chern character". Inventiones mathematicae 168, n.º 1 (8 de diciembre de 2006): 23–81. http://dx.doi.org/10.1007/s00222-006-0026-x.

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33

Takhtajan, Leon A. "Explicit computation of the Chern character forms". Geometriae Dedicata 181, n.º 1 (15 de octubre de 2015): 223–37. http://dx.doi.org/10.1007/s10711-015-0121-5.

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34

Brown, Michael y Mark Walker. "A Chern–Weil formula for the Chern character of a perfect curved module". Journal of Noncommutative Geometry 14, n.º 2 (29 de julio de 2020): 709–72. http://dx.doi.org/10.4171/jncg/378.

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35

Watanabe, Takashi. "The Chern character on the odd spinor groups". Publications of the Research Institute for Mathematical Sciences 22, n.º 3 (1986): 513–25. http://dx.doi.org/10.2977/prims/1195177848.

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36

Torii, Takeshi. "On E∞ -structure of the generalized Chern character". Bulletin of the London Mathematical Society 42, n.º 4 (17 de mayo de 2010): 680–90. http://dx.doi.org/10.1112/blms/bdq026.

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37

Chern, Shikai y Xiaodong Hu. "Equivariant Chern character for the invariant Dirac operator." Michigan Mathematical Journal 44, n.º 3 (1997): 451–73. http://dx.doi.org/10.1307/mmj/1029005782.

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38

Hu, Jianxun y Bai-Ling Wang. "Delocalized Chern character for stringy orbifold K-theory". Transactions of the American Mathematical Society 365, n.º 12 (4 de junio de 2013): 6309–41. http://dx.doi.org/10.1090/s0002-9947-2013-05834-5.

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39

Cibotaru, Daniel. "The odd Chern character and index localization formulae". Communications in Analysis and Geometry 19, n.º 2 (2011): 209–76. http://dx.doi.org/10.4310/cag.2011.v19.n2.a1.

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40

Nistor, Victor. "A Bivariant Chern character for p-summable quasihomomorphisms". K-Theory 5, n.º 3 (mayo de 1991): 193–211. http://dx.doi.org/10.1007/bf00533587.

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41

Tabuada, Gonçalo. "A universal characterization of the Chern character maps". Proceedings of the American Mathematical Society 139, n.º 04 (1 de abril de 2011): 1263. http://dx.doi.org/10.1090/s0002-9939-2010-10569-5.

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42

Watanabe, Takashi. "The Chern character of the symmetric space {$EI$}". Publications of the Research Institute for Mathematical Sciences 31, n.º 3 (1995): 533–44. http://dx.doi.org/10.2977/prims/1195164053.

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43

Tu, Jean-Louis y Ping Xu. "Chern character for twisted K-theory of orbifolds". Advances in Mathematics 207, n.º 2 (diciembre de 2006): 455–83. http://dx.doi.org/10.1016/j.aim.2005.12.001.

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44

Haution, Olivier. "Integrality of the Chern character in small codimension". Advances in Mathematics 231, n.º 2 (octubre de 2012): 855–78. http://dx.doi.org/10.1016/j.aim.2012.04.030.

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45

LAI, ALAN. "ON THE JLO COCYCLE AND ITS TRANSGRESSION IN ENTIRE CYCLIC COHOMOLOGY". International Journal of Geometric Methods in Modern Physics 10, n.º 07 (10 de junio de 2013): 1350037. http://dx.doi.org/10.1142/s0219887813500370.

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The JLO character formula due to Jaffe–Lesniewski–Osterwalder [Quantum K-theory: the Chern character, Commun. Math. Phys.112 (1988) 75–88] assigns to each Fredholm module a cocycle in entire cyclic cohomology. It descends to define a cohomological Chern character on K-homology. This paper extends the definition of the JLO character formula for Breuer–Fredholm modules, the modules that represent type II noncommutative geometry; and shows that the JLO character formula coincides with the Connes character formula [see M. Benameur and T. Fack, Type II noncommutative geometry. I. Dixmier trace in von Neumann algebras, Adv. Math.199 (2006) 29–87] at the level of entire cyclic cohomology.
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46

Balcerzak, Bogdan. "Chern–Simons forms for ℝ-linear connections on Lie algebroids". International Journal of Mathematics 29, n.º 13 (diciembre de 2018): 1850094. http://dx.doi.org/10.1142/s0129167x18500945.

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This paper considers the Chern–Simons forms for [Formula: see text]-linear connections on Lie algebroids. A generalized Chern–Simons formula for such [Formula: see text]-linear connections is obtained. We apply it to define the Chern character and secondary characteristic classes for [Formula: see text]-linear connections of Lie algebroids.
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47

Benameur, Moulay-Tahar y James L. Heitsch. "Index Theory and Non-Commutative Geometry II. Dirac Operators and Index Bundles". Journal of K-Theory 1, n.º 2 (30 de noviembre de 2007): 305–56. http://dx.doi.org/10.1017/is007011012jkt007.

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AbstractWhen the index bundle of a longitudinal Dirac type operator is transversely smooth, we define its Chern character in Haefliger cohomology and relate it to the Chern character of the K—theory index. This result gives a concrete connection between the topology of the foliation and the longitudinal index formula. Moreover, the usual spectral assumption on the Novikov-Shubin invariants of the operator is improved.
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48

Getzler, E. "The Equivariant Chern Character for Non-compact Lie Groups". Advances in Mathematics 109, n.º 1 (noviembre de 1994): 88–107. http://dx.doi.org/10.1006/aima.1994.1081.

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49

Gerenrot, Dmitry. "Residue formulation of the Chern character on smooth manifolds". Topology and its Applications 154, n.º 11 (junio de 2007): 2282–305. http://dx.doi.org/10.1016/j.topol.2007.03.004.

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50

Azmi, Fatima M. "Equivariant Bivariant Cyclic Theory and Equivariant Chern-Connes Character". Rocky Mountain Journal of Mathematics 34, n.º 2 (junio de 2004): 391–412. http://dx.doi.org/10.1216/rmjm/1181069859.

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