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PROPER
$\mathrm {CAT(0)}$ ACTIONS OF UNIPOTENT-FREE LINEAR GROUPS
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 24 / Issue 2 / March 2025
- Published online by Cambridge University Press:
- 07 January 2025, pp. 587-601
- Print publication:
- March 2025
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Let
$\Gamma $ be a finitely generated group of matrices over 
$\mathbb {C}$. We construct an isometric action of 
$\Gamma $ on a complete 
$\mathrm {CAT}(0)$ space such that the restriction of this action to any subgroup of 
$\Gamma $ containing no nontrivial unipotent elements is well behaved. As an application, we show that if M is a graph manifold that does not admit a nonpositively curved Riemannian metric, then any finite-dimensional 
$\mathbb {C}$-linear representation of 
$\pi _1(M)$ maps a nontrivial element of 
$\pi _1(M)$ to a unipotent matrix. In particular, the fundamental groups of such 3-manifolds do not admit any faithful finite-dimensional unitary representations.
Rotors in Khovanov Homology
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- Journal:
- Canadian Mathematical Bulletin / Volume 59 / Issue 1 / 01 March 2016
- Published online by Cambridge University Press:
- 20 November 2018, pp. 159-169
- Print publication:
- 01 March 2016
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