Comparison of K-theory spectral sequences, with applications

1981 ◽  
pp. 141-167 ◽  
Author(s):  
Henri Gillet
Keyword(s):  
Spectral Sequences ◽  
K Theory

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.

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory

On a question of swan in algebraic k-theory

1973 ◽  
Vol 6 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Pramod K. Sharma ◽  
Jan R. Strooker
Keyword(s):  
K Theory

scholarly journals Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin Antieau ◽  
Bhargav Bhatt ◽  
Akhil Mathew
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Characteristic P ◽  
De Rham

Abstract We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.

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