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The rack space
Author(s):
Roger
Fenn;
Colin
Rourke;
Brian
Sanderson
Journal:
Trans. Amer. Math. Soc.
359
(2007),
701-740.
MSC (2000):
Primary 55Q40, 57M25;
Secondary 57Q45, 57R15, 57R20, 57R40
Posted:
August 24, 2006
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Abstract:
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  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.
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Additional Information:
Roger
Fenn
Affiliation:
Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, United Kingdom
Email:
R.A.Fenn@sussex.ac.uk
Colin
Rourke
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
Email:
cpr@maths.warwick.ac.uk
Brian
Sanderson
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
Email:
bjs@maths.warwick.ac.uk
DOI:
10.1090/S0002-9947-06-03912-2
PII:
S 0002-9947(06)03912-2
Keywords:
Classifying space,
codimension 2,
cubical set,
James bundle,
link,
knot,
$\pi_2$,
rack
Received by editor(s):
August 1, 2003
Received by editor(s) in revised form:
November 24, 2004
Posted:
August 24, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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