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Results tagged with gt.geometric-topology
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user 20595
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
16
votes
Is {6,3,7} an 'ultrahyperbolic' Coxeter group?
Actually, every Coxeter system of rank four is either euclidean or hyperbolic. That is, the canonical bilinear form has at most one negative eigenvalue.
It follows from the paper Sphere packings and …
- 2,581
7
votes
2
answers
440
views
Are there infinitely many commensurable classes of finite-covolume hyperbolic Coxeter groups?
Allcock(2006) proved that
there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space $H^n$ for every $n\le 19$ (resp. $n\le 6$).
His main technique of …
- 2,581