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S. Prassidis

Publications and source records attributed to S. Prassidis.

6 recordsLinked to original sources
arXiv2023

Topological rigidity of quoric manifolds

Quoric manifolds are the quaternionic analogue of toric manifolds. They admit a locally nice action of $(S^3)^n$ and the quotient is a manifold with corners. We show that they satisfy equivariant rigidity. More precisely, any locally linear $(S^3)^n$-manifold that it is equivariantly homotopic equivalent to a quoric manifold is equivariantly homeomorphic to it. The proof is given by generalising the methods of used in Coxeter and toric manifolds.

math.AT↗
arXiv2014

Topological rigidity of quasitoric manifolds

Quasitoric manifolds are manifolds that admit an action of the torus that is locally as the standard action of T^n on C^n. It is known that the quotients of such actions are nice manifolds with corners. We prove that such manifolds are equivariantly rigid i.e., that any other manifold that is T^n-homotopy equivalent to a quasitoric manifold, is T^n-homeomorphic to it.

math.AT↗
arXiv2009

On the linearity of the holomorph group of a free group on two generators

Let F_n denote the free group generated by n letters. The purpose of this article is to show that Hol(F_2), the holomorph of the free group on two generators, is linear. Consequently, any split group extension of F_2 by a linear group H is linear. This result gives a large linear subgroup of Aut(F_3). A second application is that the mapping class group for genus one surfaces with two punctures is linear.

math.GR↗
arXiv2004

Roundness properties of groups

Roundness of metric spaces was introduced by Per Enflo as a tool to study uniform structures of linear topological spaces. The present paper investigates geometric and topological properties detected by the roundness of general metric spaces. In particular, we show that geodesic spaces of roundness 2 are contractible, and that a compact Riemannian manifold with roundness $>1$ must be simply connected. We then focus our investigation on Cayley graphs of finitely generated groups. One of our main results is that every Cayley graph of a free abelian group on $\geq 2$ generators has roundness $=1$. We show that if a group has no Cayley graph of roundness $=1$, then it must be a torsion group with every element of order $2,3,5$, or 7.

math.MG↗