Homology, Homotopy and Applications

Volume 16 (2014)

Number 2

Homotopy representations over the orbit category

Pages: 345 – 369

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n2.a19

Authors

Ian Hambleton (Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)

Ergün Yalçin (Department of Mathematics, Bilkent University, Bilkent, Ankara, Turkey)

Abstract

Let $G$ be a finite group. The unit sphere in a finite-dimensional orthogonal $G$-representation motivates the definition of homotopy representations, due to tom Dieck. We introduce an algebraic analogue and establish its basic properties, including the Borel-Smith conditions and realization by finite $G$-CW-complexes.

Keywords

homotopy representation, orbit category

2010 Mathematics Subject Classification

18G35, 20J05, 55U15, 57S17

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