A Remark on Alexander Duality and Thom Classes
Daniele Carlo Struppa, Cristina Turrini · Chapman University Digital Commons (Chapman University) · 1985
Let M be an n-dimensional compact oriented differentiable manifold, A subset M a closed subset, U = M\A. We associate to each (n - k)-submanifold with boundary (S,\ ensuremath {\ partial} S) $\ subset $(M, U) a <> $\ tau^{(s)}\ epsilon\ bar {H^{k}}(A) $, via Alexander duality. Thom isomorphism theorem enables us to provide an explicit construction of $\ tau^{(s)} $. Finally we discuss some concrete examples.