The rack space
| dc.creator | Fenn, Roger | |
| dc.creator | Rourke, Colin | |
| dc.creator | Sanderson, Brian | |
| dc.date | 2003-04-16 | |
| dc.date | 2003-06-15 | |
| dc.date.accessioned | 2026-07-07T04:56:58Z | |
| dc.date.available | 2026-07-07T04:56:58Z | |
| dc.description | 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 (defined in [Trunks and classifying spaces, Applied Categorical Structures, 3 (1995) 321--356]) and the classifying bundle is the first James bundle (defined in "James bundles" math.AT/0301354). 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 π_2 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. | |
| dc.description | This paper is largely extracted from our January 1996 preprint `James bundles and applications' available at http://www.maths.warwick.ac.uk/~cpr/ftp/james.ps Version 2: minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0304228 | |
| dc.identifier | http://arxiv.org/abs/math/0304228 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67110 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55Q40, 57M25; 57Q45, 57R15, 57R20, 57R40 | |
| dc.title | The rack space | |
| dc.type | text |