nLab
periodic cohomology theory

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Definition

A peridodic cohomology theory is an

even multiplicative cohomology theory EE with a Bott element βE 2(*)\beta \in E^2({*}) which is invertible (under multiplication in the cohomology ring of the point) so that multiplication by it induces an isomorphism

()β:E *(*)E *+2(*). (-)\cdot \beta : E^*({*}) \simeq E^{*+2}({*}) \,.

Compare with the notion of weakly periodic cohomology theory.

References

Lecture notes include

Revised on November 12, 2013 13:57:26 by Urs Schreiber (188.200.54.65)