Boden, Hans U. and Friedl, Stefan (2008) Metabelian SL (n, C) representations of knot groups. Pacific Journal of Mathematics, Volume 238 (Number 1). pp. 7-25. doi:10.2140/pjm.2008.238.7

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Abstract

We give a classification of irreducible metabelian representations from a knot group into SL(n, C) and GL(n, C). If the homology of the n-fold branched cover of the knot is finite, we show that every irreducible metabelian SL(n, C) representation is conjugate to a unitary representation and that the set of conjugacy classes of such representations is finite. In that case, we give a formula for this number in terms of the Alexander polynomial of the knot. These results are the higher rank generalizations of a result of Nagasato, who recently studied irreducible, metabelian SL(2, C) representations of knot groups. Finally we deduce the existence of irreducible metabelian SL(n, C) representations of the knot group for any knot with nontrivial Alexander polynomial.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Knot theory
Journal or Publication Title:	Pacific Journal of Mathematics
Publisher:	University of California, Berkeley
ISSN:	0030-8730
Official Date:	November 2008
Dates:	Date Event November 2008 Published
Volume:	Volume 238
Number:	Number 1
Number of Pages:	19
Page Range:	pp. 7-25
DOI:	10.2140/pjm.2008.238.7
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Natural Sciences and Engineering Research Council Canada (NSERC), Centre interuniversitaire de recherches en géométrie et topologie (CIRGET), Centre de recherches mathématiques (CRM), Institut des sciences mathématiques (ISM)

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