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arXiv research

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2 results for “flag-no-square”

On flag-no-square

4

-manifoldsmath.GT

New flag-no-square 4-manifolds discovered with unique triangulations.

problem Identifying 4-manifolds with specific triangulation properties.

method Introduced star-connected-sum operation to preserve flag-no-square property; derived new constructions.

result Found non-aspherical flag-no-square 4-manifolds, answering a question by Przytycki and Swiatkowski.

4-manifolds flag-no-square triangulations star-connected-sum super-exponential

2023-10-20abs ↗pdf ↗

Coxeter groups, hyperbolic cubes, and acute triangulationsmath.GT

Let $C(L)$ be the right-angled Coxeter group defined by an abstract triangulation $L$ of $\mathbb{S}^2$ . We show that $C(L)$ is isomorphic to a hyperbolic right-angled reflection group if and only if $L$ can be realized as an acute triangulation. The proof relies on the theory of CAT(-1) spaces. A corollary is that an …

2013-06-25abs ↗pdf ↗