### Fixed point theory and framed cobordism

DOI: http://dx.doi.org/10.12775/TMNA.2003.010

#### Abstract

The Thom-Pontryagin construction is

studied from the point of view of fixed point situations, and

a very natural correspondence between framed cobordism

classes and fixed point situations is given. Since

fixed point classes integrate a cohomology theory,

called $\text{\rm FIX}$, which generalizes in a natural way

to an equivariant theory, this sheds light into

possible approaches to equivariant cobordism.

studied from the point of view of fixed point situations, and

a very natural correspondence between framed cobordism

classes and fixed point situations is given. Since

fixed point classes integrate a cohomology theory,

called $\text{\rm FIX}$, which generalizes in a natural way

to an equivariant theory, this sheds light into

possible approaches to equivariant cobordism.

#### Keywords

Cobordism; fixed point index; generalized cohomology

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