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Metabelian SL (n, C) representations of knot groups
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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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Official URL: http://dx.doi.org/10.2140/pjm.2008.238.7
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, Engineering and Medicine > 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: |
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| 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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