The rack space

dc.creatorFenn, Roger
dc.creatorRourke, Colin
dc.creatorSanderson, Brian
dc.date2003-04-16
dc.date2003-06-15
dc.date.accessioned2026-07-07T04:56:58Z
dc.date.available2026-07-07T04:56:58Z
dc.descriptionThe 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.descriptionThis 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.identifierhttps://arxiv.org/abs/math/0304228
dc.identifierhttp://arxiv.org/abs/math/0304228
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67110
dc.subjectGeometric Topology
dc.subjectAlgebraic Topology
dc.subject55Q40, 57M25; 57Q45, 57R15, 57R20, 57R40
dc.titleThe rack space
dc.typetext

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