A stable range description of the space of link maps

Goodwillie, Thomas G; Munson, Brian A

doi:10.2140/agt.2010.10.1305

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A stable range description of the space of link maps

Thomas G Goodwillie and Brian A Munson

Algebraic & Geometric Topology 10 (2010) 1305–1315

DOI: 10.2140/agt.2010.10.1305

Abstract

We study the space $Link (P, Q; N)$ of link maps: maps from $P ⊔ Q$ to $N$ such that the images of $P$ and $Q$ are disjoint. We identify the homotopy fiber of the inclusion $Link (P, Q; N) \to Map (P, N) \times Map (Q, N)$ in a stable range, showing that it has a $(2 (n - p - q) - 3)$ –connected map to the infinite loopspace of a certain Thom spectrum.

Keywords

link map, linking number

Mathematical Subject Classification 2000

Primary: 57Q45

Secondary: 58D15, 57R99

References

Publication

Received: 26 October 2009

Revised: 20 February 2010

Accepted: 14 May 2010

Published: 4 June 2010

Authors

Thomas G Goodwillie
Department of Mathematics Brown University Box 1917 Providence RI 02912-0001

Brian A Munson
Department of Mathematics Wellesley College 106 Central Street Wellesley MA 02481
http://palmer.wellesley.edu/~munson

Volume 10, issue 3 (2010)