Fiber Bundles, Vector Bundles and K-Theory

2016 ◽  
pp. 197-247
Author(s):  
Mahima Ranjan Adhikari
Keyword(s):  
Vector Bundles ◽  
Fiber Bundles ◽  
K Theory

scholarly journals The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra

2019 ◽  
Vol 30 (11) ◽  
pp. 1950057 ◽  
Author(s):  
M. Izumi ◽  
T. Sogabe
Keyword(s):  
Automorphism Group ◽  
Vector Bundles ◽  
Group Structure ◽  
Cuntz Algebra ◽  
Classifying Space ◽  
Cuntz Algebras ◽  
K Theory ◽  
Continuous Fields

We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra [Formula: see text] for finite [Formula: see text] in terms of K-theory. We show that there is an example of a space for which the homotopy set is a noncommutative group, and hence, the classifying space of the automorphism group of the Cuntz algebra for finite [Formula: see text] is not an H-space. We also make an improvement of Dadarlat’s classification of continuous fields of the Cuntz algebras in terms of vector bundles.

K-Theory of Vector Bundles, of Modules, and of Idempotents

2007 ◽  
pp. 45-54
Author(s):  
D. Husemöller ◽  
M. Joachim ◽  
B. Jurčo ◽  
M. Schottenloher
Keyword(s):  
Vector Bundles ◽  
K Theory

scholarly journals Dispersive semiflows on fiber bundles

2017 ◽  
Vol 37 (2) ◽  
pp. 85-99
Author(s):  
Josiney A. Souza ◽  
Hélio V. M. Tozatti
Keyword(s):  
Periodic Point ◽  
Fiber Bundle ◽  
Vector Bundles ◽  
Base Space ◽  
Total Space ◽  
Fiber Bundles ◽  
Almost Periodic ◽  
Special Result ◽  
Almost Periodic Point

This paper studies dispersiveness of semiflows on fiber bundles. The main result says that a right invariant semiflow on a fiber bundle is dispersive on the base space if and only if there is no almost periodic point and the semiflow is dispersive on the total space. A special result states that linear semiflows on vector bundles are not dispersive.

scholarly journals Equivariant KK-theory for generalised actions and Thom isomorphism in groupoid twisted K-theory

2013 ◽  
Vol 13 (1) ◽  
pp. 83-113 ◽  
Author(s):  
El-Kaïoum M. Moutuou
Keyword(s):  
Vector Bundles ◽  
Isomorphism Theorem ◽  
Locally Compact ◽  
Bott Periodicity ◽  
C Algebras ◽  
Thom Isomorphism ◽  
K Theory ◽  
Thom Isomorphism Theorem

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.

scholarly journals Topological phases: Isomorphism, homotopy and K-theory

2015 ◽  
Vol 12 (09) ◽  
pp. 1550098 ◽  
Author(s):  
Guo Chuan Thiang
Keyword(s):  
Topological Insulators ◽  
Vector Bundles ◽  
Equivalence Classes ◽  
Topological Phases ◽  
Winding Number ◽  
Symmetry Constraints ◽  
K Theory

Equivalence classes of gapped Hamiltonians compatible with given symmetry constraints, such as those underlying topological insulators, can be defined in many ways. For the non-chiral classes modeled by vector bundles over Brillouin tori, physically relevant equivalences include isomorphism, homotopy, and K-theory, which are inequivalent but closely related. We discuss an important subtlety which arises in the chiral Class AIII systems, where the winding number invariant is shown to be relative rather than absolute as is usually assumed. These issues are then analyzed and reconciled in the language of K-theory.

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 Equivariant K-theory, groupoids and proper actions

2011 ◽  
Vol 9 (3) ◽  
pp. 475-501
Author(s):  
Jose Cantarero
Keyword(s):  
Vector Bundles ◽  
Cohomology Theory ◽  
Dimensional Vector ◽  
Lie Groupoids ◽  
Proper Actions ◽  
Lie Groupoid ◽  
Finite Dimensional ◽  
Cw Complexes ◽  
K Theory ◽  
Completion Theorem

AbstractIn this paper we define complex equivariant K-theory for actions of Lie groupoids using finite-dimensional vector bundles. For a Bredon-compatible Lie groupoid , this defines a periodic cohomology theory on the category of finite -CW-complexes. We also establish an analogue of the completion theorem of Atiyah and Segal. Some examples are discussed.

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