# nLab periodic cohomology theory

A peridodic cohomology theory is an

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

$\left(-\right)\cdot \beta :{E}^{*}\left(*\right)\simeq {E}^{*+2}\left(*\right)\phantom{\rule{thinmathspace}{0ex}}.$(-)\cdot \beta : E^*({*}) \simeq E^{*+2}({*}) \,.

Compare with the notion of weakly periodic cohomology theory.

# related entries

Revised on September 14, 2009 17:07:10 by Urs Schreiber (195.37.209.182)