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2008 A manifold calculus approach to link maps and the linking number
Brian A Munson
Algebr. Geom. Topol. 8(4): 2323-2353 (2008). DOI: 10.2140/agt.2008.8.2323


We study the space of link maps Link(P1,,Pk;N), the space of smooth maps P1PkN such that the images of the Pi 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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Brian A Munson. "A manifold calculus approach to link maps and the linking number." Algebr. Geom. Topol. 8 (4) 2323 - 2353, 2008.


Received: 16 April 2008; Revised: 30 October 2008; Accepted: 3 November 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1168.57018
MathSciNet: MR2465743
Digital Object Identifier: 10.2140/agt.2008.8.2323

Primary: 57Q45, 57R99
Secondary: 55P99, 57M25

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.8 • No. 4 • 2008
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