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Abstract
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We study the space of link maps ,
the space of smooth maps
such that the images of the
are pairwise disjoint. We apply the manifold calculus of functors developed by
Goodwillie and Weiss to study the difference between it and its linear and quadratic
approximations. We identify an appropriate generalization of the linking number as
the geometric object which measures the difference between the space of link
maps and its linear approximation. Our analysis of the difference between
link maps and its quadratic approximation resembles recent work of the
author on embeddings, and is used to show that the Borromean rings are
linked.
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Keywords
calculus of functors, link map, linking number
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Mathematical Subject Classification 2000
Primary: 57Q45, 57R99
Secondary: 55P99, 57M25
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Publication
Received: 16 April 2008
Revised: 30 October 2008
Accepted: 3 November 2008
Published: 20 December 2008
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