Coda: The Bott periodicity theorem

2015 ◽  
pp. 169-180
Keyword(s):  
Bott Periodicity ◽  
Periodicity Theorem

Delooping the total Stiefel–Whitney class

1988 ◽  
Vol 103 (1) ◽  
pp. 83-87
Author(s):  
A. Kozlowski
Keyword(s):  
Loop Space ◽  
Cohomology Ring ◽  
Group Homomorphism ◽  
Double Loop ◽  
Bott Periodicity ◽  
Group Of Units ◽  
Periodicity Theorem ◽  
Whitney Class ◽  
Infinite Loop ◽  
Infinite Loop Space

Let FH(X) denote the group of units of the classical cohomology ring H(X) = Πn≥0Hn(X; Z/2) of a CW-complex X. The total Stiefel–Whitney class can be viewed as a group homomorphism where is the reduced real K-theory of X. Both and FH( ) are representable functors, with representing spaces BO and FH, and thus w can be represented by a map w: BO → FH. By the Bott periodicity theorem, BO is an infinite loop space, and by a theorem of G. Segal[9] so is FH. However, it is well known that w is not an infinite loop map; this was first shown in [10]. The purpose of this paper is to prove the following:Theorem 0·1. w: BO → FHis a loop map but not a double loop map.

Plans’ Periodicity Theorem for Jacobian of Circulant Graphs

2021 ◽  
Vol 103 (3) ◽  
pp. 139-142
Author(s):  
A. D. Mednykh ◽  
I. A. Mednykh
Keyword(s):  
Circulant Graphs ◽  
Periodicity Theorem

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
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