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This subtopic studies topological K-theory, emphasizing vector bundles, Bott periodicity, and stable phenomena in topology.
19K14 studies $k_0$ as an ordered group, traces in topological K-theory. It studies vector bundles and generalized cohomology theories through topological and homotopy-theoretic constructions.
Topological K-Theory (Wikipedia)
Used to classify vector bundles, compute index-theoretic invariants, and organize generalized cohomology.
19K33 studies ext and $k$-homology in topological K-theory. It studies vector bundles and generalized cohomology theories through topological and homotopy-theoretic constructions.
Topological K-Theory (Wikipedia)
Used to classify vector bundles, compute index-theoretic invariants, and organize generalized cohomology.
19K35 studies kasparov theory ($kk$-theory) in topological K-theory. It studies vector bundles and generalized cohomology theories through topological and homotopy-theoretic constructions.
Topological K-Theory (Wikipedia)
Used to classify vector bundles, compute index-theoretic invariants, and organize generalized cohomology.
19K56 studies index theory in topological K-theory. It studies vector bundles and generalized cohomology theories through topological and homotopy-theoretic constructions.
Topological K-Theory (Wikipedia)
Used to classify vector bundles, compute index-theoretic invariants, and organize generalized cohomology.