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Given a hyperbolic knot K and any n ≥ 2 the abelian representations and the holonomy representation each give rise to an (n−1)–dimensional component in the SL(n, ℂ)–character variety. A component of the SL(n, ℂ)–character variety of dimension ≥ n is called high-dimensional.
It was proved by D Cooper and D Long that there exist hyperbolic knots with high-dimensional components in the SL(2, ℂ)–character variety. We show that given any nontrivial knot K and sufficiently large n the SL(n, ℂ)–character variety of K admits high-dimensional components.
Keywords: knots, character, knot groups, representations
Friedl, Stefan 1 ; Heusener, Michael 2
@article{10_2140_agt_2018_18_313,
author = {Friedl, Stefan and Heusener, Michael},
title = {On high-dimensional representations of knot groups},
journal = {Algebraic and Geometric Topology},
pages = {313--332},
publisher = {mathdoc},
volume = {18},
number = {1},
year = {2018},
doi = {10.2140/agt.2018.18.313},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.313/}
}
TY - JOUR AU - Friedl, Stefan AU - Heusener, Michael TI - On high-dimensional representations of knot groups JO - Algebraic and Geometric Topology PY - 2018 SP - 313 EP - 332 VL - 18 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.313/ DO - 10.2140/agt.2018.18.313 ID - 10_2140_agt_2018_18_313 ER -
%0 Journal Article %A Friedl, Stefan %A Heusener, Michael %T On high-dimensional representations of knot groups %J Algebraic and Geometric Topology %D 2018 %P 313-332 %V 18 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.313/ %R 10.2140/agt.2018.18.313 %F 10_2140_agt_2018_18_313
Friedl, Stefan; Heusener, Michael. On high-dimensional representations of knot groups. Algebraic and Geometric Topology, Tome 18 (2018) no. 1, pp. 313-332. doi: 10.2140/agt.2018.18.313
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