Induced character in equivariant K-theory and wreath products

2019/02/19 by Germán Combariza, Combariza, Germán, Juan Rodríguez +4
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.KT

paper · pdf · doi:10.48550/arxiv.1902.07097

New version with minor changes

arxiv created 2019/11/20 · arxiv updated 2019/11/21

Abstract

Let G be a finite group, X be a compact G-space. In this note we study the (ℤ_ + ×ℤ/2ℤ)-graded algebra F^q_G(X) = \bigoplus_n≥0 qⁿ ⋅ K_G\wr\mathfrakS_n(Xⁿ)⊗ℂ, defined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra. More specifically, let H be another finite group and Y be a compact H-space, we give a decomposition of F^q_{G× H}(X× Y) in terms of F^q_G(X) and F^q_H(Y). For this, we need to study the representation theory of pullbacks of groups. We discuss also some applications of the above result to equivariant connective K-homology.

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