Bott periodicity and the 𝑄-construction

1996 ◽  
pp. 107-124 ◽  
Author(s):  
Charles H. Giffen
Keyword(s):  
Bott Periodicity

Bott Periodicity Maps and Clifford Algebras

2007 ◽  
pp. 175-188
Author(s):  
D. Husemöller ◽  
M. Joachim ◽  
B. Jurčo ◽  
M. Schottenloher
Keyword(s):  
Clifford Algebras ◽  
Bott Periodicity

Bott Periodicity

2010 ◽  
pp. 185-208
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
Bott Periodicity

On the relation of connective K-theory to homology

1970 ◽  
Vol 68 (3) ◽  
pp. 637-639 ◽  
Author(s):  
Larry Smith
Keyword(s):  
Exact Sequence ◽  
Natural Transformation ◽  
Homology Theory ◽  
Finite Complex ◽  
Ring Spectrum ◽  
Bott Periodicity ◽  
Ring Spectra ◽  
K Theory ◽  
Image Position ◽  
Natural Way

Let us denote by k*( ) the homology theory determined by the connective BU spectrum, bu, that is, in the notations of (1) and (9), bu2n = BU(2n,…,∞), bu2n+1 = U(2n + 1,…, ∞) with the spectral maps induced via Bott periodicity. The resulting spectrum, bu, is a ring spectrum. Recall that k*(point) ≅ Z[t], degree t = 2. There is a natural transformation of ring spectrainducing a morphismof homology functors. It is the objective of this note to establish: Theorem. Let X be a finite complex. Then there is a natural exact sequencewhere Z is viewed as a Z[t] module via the augmentationand, is induced by η*in the natural way.

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 Bott periodicity via simplicial spaces

1980 ◽  
Vol 62 (2) ◽  
pp. 450-454 ◽  
Author(s):  
Bruno Harris
Keyword(s):  
Bott Periodicity
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