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4 votes
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Bott periodicity homeomorphisms for spaces of Clifford extensions

I am trying to prove the following statement of real Bott periodicity, on the level of actual spaces of Clifford module extensions (i.e., not equivalence classes of modules). Let $W = \mathbb{R}^{\in …
Matt C's user avatar
  • 151
1 vote

Bott periodicity homeomorphisms for spaces of Clifford extensions

I believe I have the idea of a proof. Apologies for the mess - hopefully it is somewhat intelligible (and somewhat correct). We follow the form of this isomorphism: $Cl_{n+8} \cong Cl_n\otimes_\math …
Matt C's user avatar
  • 151
8 votes
1 answer
231 views

What is the inverse in K-theory represented by Clifford module extensions?

I am working on a model for topological KO-theory which is represented by explicit spaces of orthogonal Clifford module extensions. That is, assuming $M$ compact, $KO^{-n+1}(M) := [M,X_n]$ where the …
Matt C's user avatar
  • 151
2 votes
Accepted

What is the inverse in K-theory represented by Clifford module extensions?

For what it's worth, I did eventually get the answer. The idea is to notice that if $\overline{W}$ denotes the background Clifford module $W$ (above $\mathbb{R}^n$) endowed with the opposite module s …
Matt C's user avatar
  • 151