The rack space

Fenn, Roger, Rourke, Colin and Sanderson, Brian (2007) The rack space. Transactions of the American Mathematical Society, 359 (2). pp. 701-740. ISSN 0002-9947

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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 π2 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Roger Fenn
Date Deposited: 15 Feb 2013 10:17
Last Modified: 02 Jul 2019 20:38

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