Equivariant Stable Homotopy Theory

Greenlees, J. P. C.; May, J. P.

doi:10.1016/b978-044481779-2/50009-2

Cited by 40 publications

(35 citation statements)

References 52 publications

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“…In equivariant homotopy theory, the role of "abelian group" is played by the notion of a Mackey functor (Dress [18]). The following is the summary of Dress' definition as it appears in Greenlees-May [26].…”

Section: 54mentioning

confidence: 99%

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On the nonexistence of elements of Kervaire invariant one

2016

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Section: 54mentioning

confidence: 99%

“…The definitions, proofs, constructions, and other details are explained in Appendices A and B. The reader is also referred to the books of tom Dieck [80,79], and the survey of Greenlees and May [26] for an overview of equivariant stable homotopy theory, and for further references.…”

Section: Equivariant Stable Homotopy Theorymentioning

confidence: 99%

On the nonexistence of elements of Kervaire invariant one

2016

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“…For a construction of the representing spectra, see e.g. [14]. We write H for the spectrum representing ordinary cohomology.…”

Section: Preliminariesmentioning

confidence: 99%

Equivariant Lefschetz and Fuller indices via topological intersection theory

Wruck

2015

Topology and its Applications

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Available online xxxx MSC: 55N91 55M20 Keywords: Equivariant intersection theory Equivariant Lefschetz number Equivariant Fuller index Equivariant fixed point theoryFor a compact Lie group G, we use G-equivariant Poincaré duality for ordinary RO(G)-graded homology to define an equivariant intersection product, the dual of the equivariant cup product. Using this, we give a homological construction of the equivariant Lefschetz number and a simple proof of the equivariant Lefschetz fixed point theorem. We relate this invariant to existing notions of equivariant Lefschetz numbers and give an explicit computational formula. Using similar techniques, we also construct an equivariant Fuller index with values in the rationalized Burnside ring.

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“…Let a V denote the inclusion of S 0 = {0, ∞} into S V . This class is a kind of Euler class [13]. Multiplication by a V gives us a map A → π 0 S V , and this realizes the above isomorphism.…”

Section: Some Equivariant Homotopy Groupsmentioning

confidence: 99%