The linear isometries operad in Lie--Tate homology
Pelle Salomonsson
TL;DR
This paper provides a simplified description of the product in negative Tate-cohomology for compact Lie groups and discusses the action of the Dyer--Lashof algebra via the linear-isometries operad.
Contribution
It offers an independent and simplified framework for understanding the product structure in negative Tate-cohomology and its algebraic actions.
Findings
Describes the product in negative Tate-cohomology for compact Lie groups.
Explains the action of the Dyer--Lashof algebra using the linear-isometries operad.
Provides a conceptual, rather than computational, perspective.
Abstract
We give an independent, and perhaps somewhat simplified, description of the product in negative Tate-cohomology (the generalised version for compact Lie-groups). We describe, but do not compute, the corresponding action of the Dyer--Lashof-algebra, using the linear-isometries operad.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models