Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article

Loop spaces and the compression theorem

Author(s): Bert Wiest
Journal: Proc. Amer. Math. Soc. 128 (2000), 3741-3747.
MSC (2000): Primary 55P35, 57M27; Secondary 57R25, 55R37
Posted: June 7, 2000
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

For a smooth, finite-dimensional manifold with a submanifold we study the topology of the straight loop space $\Omega^{st}_SM$ , the space of loops whose intersections with are subject to a certain transversality condition. Our main tool is Rourke and Sanderson's compression theorem. We prove that the homotopy type of the straight loop space of a link in depends only on the number of link components.

References:

1.: R. Fenn, C. Rourke, B. Sanderson, James bundles and applications, Warwick preprint (1996), or http://www.maths.warwick.ac.uk/ $\sim$ cpr.
2.: T. Ganea, A generalisation of the homology and homotopy suspension, Comm. Math. Helv. 39 (1965), 295-322. MR 31:4033
3.: J. Hempel, 3-manifolds, Ann. of Math. Studies 86, Princeton University Press (1976). MR 54:3702
4.: I. James, Reduced product spaces, Ann. Math. 62 (1955), 170-197. MR 17:396b
5.: C. Rourke, B. Sanderson, The compression theorem, to appear in the Ann. Math. , or http://www.maths.warwick.ac.uk/ $\sim$ cpr.
6.: B. Wiest, PhD thesis, Warwick (1997), see also http:// protis.univ-mrs.fr/ $\sim$ bertw.
7.: B. Wiest, Rack spaces and loop spaces, to appear in J. Knot Teory Ram. CMP 99:08

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 55P35, 57M27, 57R25, 55R37

Retrieve articles in all Journals with MSC (2000): 55P35, 57M27, 57R25, 55R37

Additional Information:

Bert Wiest
Affiliation: CMI, Université de Provence, 39 Rue Joliot Curie, 13453 Marseille cedex 13, France
Email: bertw@gyptis.univ-mrs.fr

DOI: 10.1090/S0002-9939-00-05472-1
PII: S 0002-9939(00)05472-1
Keywords: Compression theorem, straight loop space, rack, quandle, rack space
Received by editor(s): June 18, 1998
Received by editor(s) in revised form: February 19, 1999
Posted: June 7, 2000
Additional Notes: The author was supported by a University of Warwick Graduate Award.
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2000, American Mathematical Society


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS