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LOOP HOMOLOGY AS FIBREWISE HOMOLOGY

Published online by Cambridge University Press:  04 February 2008

M. C. Crabb
M. C. Crabb
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, UK ([email protected])
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Abstract

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The loop homology ring of an oriented closed manifold, defined by Chas and Sullivan, is interpreted as a fibrewise homology Pontrjagin ring. The basic structure, particularly the commutativity of the loop multiplication and the homotopy invariance, is explained from the viewpoint of the fibrewise theory, and the definition is extended to arbitrary compact manifolds.

Keywords

Primary 55R7055P43fibrewise homologyChas–Sullivan loop homologyPontrjagin ring
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 1 , February 2008 , pp. 27 - 44
Copyright
Copyright © Edinburgh Mathematical Society 2008