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Equivariant complex bundles, fixed points and equivariant unitary bordism

Andrés Ángel, José Manuel Gómez and Bernardo Uribe

Algebraic & Geometric Topology 18 (2018) 4001–4035

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.

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equivariant $K$–theory, twisted $K$–theory, twisted equivariant $K$–theory, equivariant bordism
Mathematical Subject Classification 2010
Primary: 19L47, 19L50, 55N22, 57R77, 57R85
Received: 15 November 2017
Revised: 8 April 2018
Accepted: 3 July 2018
Published: 11 December 2018
Andrés Ángel
Departamento de Matemáticas
Universidad de los Andes
Departamento de Matemáticas y Estadística
Universidad del Norte
José Manuel Gómez
Escuela de Matemáticas
Universidad Nacional de Colombia sede Medellín
Bernardo Uribe
Departamento de Matemáticas y Estadística
Universidad del Norte