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periodic cohomology theory

A peridodic cohomology theory is an

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

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

Compare with the notion of weakly periodic cohomology theory.

related entries

• A Survey of Elliptic Cohomology - cohomology theories