Dress induction and the Burnside quotient Green ring

Hambleton, Ian; Taylor, Laurence; Williams, Bruce

doi:10.2140/ant.2009.3.511

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Dress induction and the Burnside quotient Green ring

Ian Hambleton, Laurence R. Taylor and Bruce Williams

Vol. 3 (2009), No. 5, 511–541

DOI: 10.2140/ant.2009.3.511

Abstract

We define and study the Burnside quotient Green ring of a Mackey functor, introduced in our 1990 MSRI preprint. Some refinements of Dress induction theory are presented, together with applications to computation results for $K$ -theory and $L$ -theory of finite and infinite groups.

Keywords

Dress induction, Mackey functors, surgery obstruction groups

Mathematical Subject Classification 2000

Primary: 20C15

Secondary: 18F25, 57R67, 19A22

Milestones

Received: 27 March 2008

Revised: 1 May 2009

Accepted: 4 May 2009

Published: 9 November 2009

Authors

Ian Hambleton
McMaster University Department of Mathematics & Statistics Hamilton, ON L8S 4K1 Canada

Laurence R. Taylor
University of Notre Dame Department of Mathematics Notre Dame, IN 46556 United States

Bruce Williams
University of Notre Dame Department of Mathematics Notre Dame, IN 46556 United States

Vol. 3, No. 5, 2009