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fibrewise homology

Proceedings of the Edinburgh Mathematical Society (1)

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LOOP HOMOLOGY AS FIBREWISE HOMOLOGY
M. C. Crabb
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 51 / Issue 1 / February 2008

Published online by Cambridge University Press:

04 February 2008, pp. 27-44
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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.