duality

# Contents

## Idea

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

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

## Referenes

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

Revised on February 9, 2016 06:45:51 by Urs Schreiber (31.55.4.24)