topological K theory

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topological K theory

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Relation to Bott Periodicity:

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Relation to algebraic K theory via the Serre-Swan theorem: attachments/Pasted%20image%2020220527233028.png

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Infty cat definition

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Some properties: attachments/Pasted%20image%2020220510161336.png

Classical

See HH and Topological cyclic homology, cyclotomic trace, coherent cohomoloy. attachments/Pasted%20image%2020220323170712.png

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Classifying space

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Stability

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Products

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E_infty space structure

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Adjoint bundles

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Examples

Setup for Bott Periodicity:

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Problems

See Hopf invariant one and hairy ball theorem. attachments/Pasted%20image%2020220527232539.png

Links to this page

unresolved links output

coherent cohomoloy in Unsorted/topological K theory

cyclotomic trace in Unsorted/topological K theory
prismatic cohomology

p-adic etale K theory
equivariant K theory

topological K theory
cohomolology theory

topological K theory
Thom space

Relation to topological K theory:
K-Theory

Algebraic K is analogous to \({\operatorname{KU}}\), complex topological K theory, or \({\operatorname{KO}}\), real topological K-theory.
K theory in AG

Relation to topological K theory:
H-space

\({\mathbf{B}}{\operatorname{U}}\times {\mathbf{Z}}\), see topological K theory.

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