Volume 11, issue 2 (2007)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Homotopical intersection theory I

John R Klein and E Bruce Williams

Geometry & Topology 11 (2007) 939–977

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
References
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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