Vector bundle classification

Layer 0 — Mathematicsin the Differential Geometry subtree

Real / complex rank-k vector bundles over CW-complex X classified by homotopy classes [X, BO(k)] / [X, BU(k)]; Chern classes c_i in H^(2i)(X; Z) characteristic invariants.

Related concepts

Expectation E[X]
Dirac operator
Spectral theorem (self-adjoint)
Peter-Weyl theorem
Homotopy equivalence (detail)
Chern classes (1946)
Z₂ topological insulator
Berry curvature in photonic bands
Non-Hermitian skin effect (Yao-Wang)
TI Bi2Se3 / Bi2Te3 (Zhang-Hasan 2009)

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