Homotopical intersection theory I

Klein, John R; Williams, E Bruce

doi:10.2140/gt.2007.11.939

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Homotopical intersection theory I

John R Klein and E Bruce Williams

Geometry & Topology 11 (2007) 939–977

DOI: 10.2140/gt.2007.11.939

arXiv: math.AT/0512479

Abstract

We give a new approach to intersection theory. Our “cycles” are closed manifolds mapping into compact manifolds and our “intersections” are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems resemble those of Hatcher and Quinn but our proofs are fundamentally different.
Errata Minor errors were corrected on page 967 (18 February 2008).

Keywords

intersection, Poincaré duality, bordism

Mathematical Subject Classification 2000

Primary: 57R19

Secondary: 55N45

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Publication

Received: 22 December 2005

Revised: 22 May 2006

Accepted: 21 January 2007

Published: 30 May 2007

Proposed: Steve Ferry

Seconded: Ralph Cohen, Peter Teichner

Authors

John R Klein
Wayne State University Detroit MI 48202 USA

E Bruce Williams
University of Notre Dame Notre Dame IN 46556 USA

Volume 11, issue 2 (2007)