S0002-9947-06-03912-2.pdf (641.05 kB)
The rack space
journal contribution
posted on 2023-06-08, 08:15 authored by Roger Fenn, Colin Rourke, Brian SandersonThe 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 SocietyISSN
0002-9947Publisher
American Mathematical SocietyPublisher URL
Issue
2Volume
359Page range
701-740Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes