What question did this study set out to answer?

Investigate the functor assigning a complex oriented cohomology ring to the classifying space of a finite group using generalized character theory.

April 26, 2000Journal of the American Mathematical SocietyOpen Access

Generalized group characters and complex oriented cohomology theories

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Authors

MHMichael J. HopkinsHarvard University NKNicholas J. KuhnUniversity of Virginia DRDouglas C. RavenelNew Mexico State University

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Implication

Theoretical study demonstrates generalized character rings for complex oriented cohomology in finite group classifying spaces, highlighting connections to formal group theory.

Key Points

Investigate the functor assigning a complex oriented cohomology ring to the classifying space of a finite group using generalized character theory.
Formulated an analogue of Artin's induction theorem using abelian subgroups as detecting families modulo group-order torsion.
Constructed a character ring of class functions on n-tuples of commuting p-power elements using Lubin–Tate formal group theory.
Computed Morava K-theory Euler characteristics and degree distributions for classifying spaces of finite groups and finite G-CW complexes.
Proved that abelian subgroups detect complex oriented cohomology of classifying spaces modulo torsion dividing the order of the group.
Calculated the nth Morava K-theory Euler characteristic of BG to equal the number of G-orbits in the set of n-tuples of p-power order elements.
Established that Morava K-theory is concentrated in even degrees for several group families, including all symmetric groups.

Cite This Study

Hopkins et al. (2000) studied this question.

synapsesocial.com/papers/69da2615387cf7069868657f https://doi.org/10.1090/s0894-0347-00-00332-5

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Implication

Theoretical study demonstrates generalized character rings for complex oriented cohomology in finite group classifying spaces, highlighting connections to formal group theory.

Generalized group characters and complex oriented cohomology theories

Discussion

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Implication

Key Points

Cite This Study

Generalized group characters and complex oriented cohomology theories

Discussion

Member takes

Implication

Key Points

Cite This Study

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