Morava K-theory rings for the modular groups in Chern classes

K-Theory ◽  
2008 ◽  
Vol 38 (2) ◽  
pp. 87-94 ◽  
Author(s):  
Malkhaz Bakuradze
Keyword(s):  
Chern Classes ◽  
Modular Groups ◽  
K Theory

scholarly journals Transferred Chern classes in Morava $K$-theory

2003 ◽  
Vol 132 (6) ◽  
pp. 1855-1860 ◽  
Author(s):  
Malkhaz Bakuradze ◽  
Stewart Priddy
Keyword(s):  
Chern Classes ◽  
K Theory

Adams operations on the virtual K-theory of ℙ(1,n)

2016 ◽  
Vol 16 (08) ◽  
pp. 1750149
Author(s):  
Takashi Kimura ◽  
Ross Sweet
Keyword(s):  
Cotangent Bundle ◽  
Crepant Resolution ◽  
Chern Classes ◽  
Localization Theorem ◽  
Virtual Line ◽  
Power Operations ◽  
Power Operation ◽  
K Theory ◽  
Line Elements ◽  
Adams Operations

We analyze the structure of the virtual (orbifold) [Formula: see text]-theory ring of the complex orbifold [Formula: see text] and its virtual Adams (or power) operations, by using the non-Abelian localization theorem of Edidin–Graham [D. Edidin and W. Graham, Nonabelian localization in equivariant [Formula: see text]-theory and Riemann–Roch for quotients, Adv. Math. 198(2) (2005) 547–582]. In particular, we identify the group of virtual line elements and obtain a natural presentation for the virtual [Formula: see text]-theory ring in terms of these virtual line elements. This yields a surjective homomorphism from the virtual [Formula: see text]-theory ring of [Formula: see text] to the ordinary [Formula: see text]-theory ring of a crepant resolution of the cotangent bundle of [Formula: see text] which respects the Adams operations. Furthermore, there is a natural subring of the virtual K-theory ring of [Formula: see text] which is isomorphic to the ordinary K-theory ring of the resolution. This generalizes the results of Edidin–Jarvis–Kimura [D. Edidin, T. J. Jarvis and T. Kimura, Chern classes and compatible power operation in inertial [Formula: see text]-theory, Ann. K-Theory (2016)], who proved the latter for [Formula: see text].

scholarly journals Chern classes for twisted K-theory

2006 ◽  
Vol 206 (1-2) ◽  
pp. 153-188 ◽  
Author(s):  
Mark E. Walker
Keyword(s):  
Chern Classes ◽  
K Theory

scholarly journals Perfect forms, K-theory and the cohomology of modular groups

2013 ◽  
Vol 245 ◽  
pp. 587-624 ◽  
Author(s):  
Philippe Elbaz-Vincent ◽  
Herbert Gangl ◽  
Christophe Soulé
Keyword(s):  
Modular Groups ◽  
K Theory

scholarly journals A version of smooth K-theory adapted to the total Chern class

2010 ◽  
Vol 6 (2) ◽  
pp. 197-230 ◽  
Author(s):  
Alain Berthomieu
Keyword(s):  
Chern Class ◽  
Chern Character ◽  
Chern Classes ◽  
New Model ◽  
K Theory ◽  
Chern Simons ◽  
Natural Way

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].

scholarly journals NET BUNDLES OVER POSETS AND K-THEORY

2013 ◽  
Vol 24 (01) ◽  
pp. 1350001 ◽  
Author(s):  
JOHN E. ROBERTS ◽  
GIUSEPPE RUZZI ◽  
EZIO VASSELLI
Keyword(s):  
Partially Ordered Sets ◽  
Fiber Bundles ◽  
Chern Classes ◽  
Ordered Sets ◽  
Partially Ordered ◽  
K Theory ◽  
Formal Properties ◽  
The Given ◽  
Homotopy Groupoid

We continue studying net bundles over partially ordered sets (posets), defined as the analogues of ordinary fiber bundles. To this end, we analyze the connection between homotopy, net homology and net cohomology of a poset, giving versions of classical Hurewicz theorems. Focusing our attention on Hilbert net bundles, we define the K-theory of a poset and introduce functions over the homotopy groupoid satisfying the same formal properties as Chern classes. As when the given poset is a base for the topology of a space, our results apply to the category of locally constant bundles.

scholarly journals Topological T-duality for torus bundles with monodromy

2015 ◽  
Vol 27 (03) ◽  
pp. 1550008
Author(s):  
David Baraglia
Keyword(s):  
Sufficient Conditions ◽  
General Setting ◽  
Spectral Sequences ◽  
Chern Classes ◽  
Courant Algebroids ◽  
Torus Bundles ◽  
Twisted Cohomology ◽  
K Theory ◽  
Definition Of ◽  
Necessary And Sufficient

We give a simplified definition of topological T-duality that applies to arbitrary torus bundles. The new definition does not involve Chern classes or spectral sequences, only gerbes and morphisms between them. All the familiar topological conditions for T-duals are shown to follow. We determine necessary and sufficient conditions for existence of a T-dual in the case of affine torus bundles. This is general enough to include all principal torus bundles as well as torus bundles with arbitrary monodromy representations. We show that isomorphisms in twisted cohomology, twisted K-theory and of Courant algebroids persist in this general setting. We also give an example where twisted K-theory groups can be computed by iterating T-duality.

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