Browder’s theorem and manifolds with corners
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چکیده
Duality and the Wu classes. The “Spanier-Whitehead dual” of a spectrum X is the function spectrum (in which S denotes the sphere spectrum) DX = F (X,S) (which exists by Brown representability). It comes equipped with an “evaluation” pairing DX ∧X → S. Write H∗(−) for homology with F2 coefficients. If X is finite, then the induced pairing H−∗(DX)⊗H∗(X)→ F2 is perfect, so there is an isomorphism Hi(X)→ Hom(H−i(DX),F2) which may be rewritten using the universal coefficient theorem as
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