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Additive power operations in equivariant cohomology, I

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Speaker: 
Nathaniel Stapleton
Affiliation: 
University of Kentucky/MPIM
Date: 
Mon, 2020-02-17 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Well-behaved multiplicative cohomology theories are equipped with power operations, multiplicative maps generalizing the m-fold product. The power operations are multiplicative, but only become additive, that is maps of rings, after collapsing a certain transfer ideal. In this talk, I will discuss the analogous story for power operations in the equivariant context. I will introduce Mackey and Green functors, equivariant analogues of abelian groups and commutative rings, and provide examples from equivariant homotopy theory. Then I will describe an explicit minimal ideal that must be collapsed in order to ensure that the power operation in the equivariant context is a map of Green functors. This is joint work with Peter Bonventre and Bert Guillou.

 
 
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