The fact that for a manifold XX of dimension kk, then for any embedding ι:X n\iota \colon X\hookrightarrow \mathbb{R}^n (which exists by the Whitney embedding theorem) the Thom space X νX^{\nu} of the normal bundle ν\nu behaves like a dual to X +X_+ under smash product of pointed topological spaces.

Under passing to suspension spectra this becomes Atiyah duality in stable homotopy theory.


For ex-spaces see around def. 1.4.2 of

  • Kate Ponto, Fixed point theory and trace for bicategories (pdf)

For parametrized spectra see page xyz of

Last revised on February 9, 2016 at 06:45:51. See the history of this page for a list of all contributions to it.