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The rack space

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posted on 2023-06-08, 08:15 authored by Roger Fenn, Colin Rourke, Brian Sanderson
The main result of this paper is a new classification theorem for links (smooth embeddings in codimension 2). The classifying space is the rack space and the classifying bundle is the first James bundle. We investigate the algebraic topology of this classifying space and report on calculations given elsewhere. Apart from defining many new knot and link invariants (including generalised James-Hopf invariants), the classification theorem has some unexpected applications. We give a combinatorial interpretation for p2 of a complex which can be used for calculations and some new interpretations of the higher homotopy groups of the 3-sphere. We also give a cobordism classification of virtual links.

History

Publication status

  • Published

File Version

  • Published version

Journal

Transactions of the American Mathematical Society

ISSN

0002-9947

Publisher

American Mathematical Society

Issue

2

Volume

359

Page range

701-740

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-02-15

First Open Access (FOA) Date

2013-02-15

First Compliant Deposit (FCD) Date

2013-02-15

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