Algebraic & Geometric Topology

Equivariant complex bundles, fixed points and equivariant unitary bordism

Andrés Ángel, José Manuel Gómez, and Bernardo Uribe

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Abstract

We study the fixed points of the universal G –equivariant complex vector bundle of rank n and obtain a decomposition formula in terms of twisted equivariant universal complex vector bundles of smaller rank. We use this decomposition to describe the fixed points of the complex equivariant K–theory spectrum and the equivariant unitary bordism groups for adjacent families of subgroups.

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 7 (2018), 4001-4035.

Dates
Received: 15 November 2017
Revised: 8 April 2018
Accepted: 3 July 2018
First available in Project Euclid: 18 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.agt/1545102060

Digital Object Identifier
doi:10.2140/agt.2018.18.4001

Mathematical Reviews number (MathSciNet)
MR3892237

Zentralblatt MATH identifier
07006383

Subjects
Primary: 19L47: Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91] 19L50: Twisted $K$-theory; differential $K$-theory 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] 57R77: Complex cobordism (U- and SU-cobordism) [See also 55N22] 57R85: Equivariant cobordism

Keywords
equivariant $K$–theory twisted $K$–theory twisted equivariant $K$–theory equivariant bordism

Citation

Ángel, Andrés; Gómez, José Manuel; Uribe, Bernardo. Equivariant complex bundles, fixed points and equivariant unitary bordism. Algebr. Geom. Topol. 18 (2018), no. 7, 4001--4035. doi:10.2140/agt.2018.18.4001. https://projecteuclid.org/euclid.agt/1545102060


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