Algebraic & Geometric Topology

A manifold calculus approach to link maps and the linking number

Brian A Munson

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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.

Article information

Algebr. Geom. Topol., Volume 8, Number 4 (2008), 2323-2353.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25} 57R99: None of the above, but in this section
Secondary: 55P99: None of the above, but in this section 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

calculus of functors link map linking number


Munson, Brian A. A manifold calculus approach to link maps and the linking number. Algebr. Geom. Topol. 8 (2008), no. 4, 2323--2353. doi:10.2140/agt.2008.8.2323.

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