Related papers: On the groupoid of transformations of rigid struct…

This thesis contains various results on unitary 2-representations of finite groups and their 2-characters, as well as on pivotal structures for fusion categories. The motivation is extended topological quantum field theory (TQFT), where the…

We prove that rigid representations of the fundamental group of a surface into the group of oreintation-preserving homeomorphisms of the circle are geometric, thereby establishing a converse statement of a theorem by the first author.

In response to a question raised by Belolipetsky and the first author, we prove that for every finite group $G$ there are infinitely many isomorphism classes of compact complex hyperbolic $2$-manifolds with automorphism group isomorphic to…

This paper contains some basic results on 2-groupoids, with special emphasis on computing derived mapping 2-groupoids between 2-groupoids and proving their invariance under strictification. Some of the results proven here are presumably…

We give an overview over several constructions of TQFT's over finite fields and cyclotomic integers and their applications to characterizing 3-manifolds and their fundamental groups.

Surface groups are known to be the Poincar\'e Duality groups of dimension two since the work of Eckmann, Linnell and M\"uller. We prove a prosolvable analogue of this result that allows us to show that surface groups are profinitely (and…

This paper gives a quick overview of the author's recent result that all finitely presented groups are QSF.

In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.

We generalize Wagoner's representation of the automorphism group of a two-sided subshifts of finite type as the fundamental group of a certain CW-complex to groupoids having a certain refinement structure. This significantly streamlines the…

In this work we study B-field transformations of multiplicative Poisson bivectors on a Lie groupoid G. We are concerned with B-fields given by multiplicative closed 2-forms on G. We view Poisson groupoids and their B-field symmetries as…

We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving…

Groups associated to surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called ramification structure. In this paper, we prove that infinitely many…

Recent results on finite open group transformations are reviewed.

We give a topological interpretation of the core group invariant of a surface embedded in S^4. We show that the group is isomorphic to the free product of the fundamental group of the double branch cover of S^4 with the surface as a…

For a K3 surface over a field of characteristic 2 which is finitely generated over its prime subfield, we prove that the cokernel of the natural map from the Brauer group of the base field to that of the K3 surface is finite modulo the…

We describe a method to implement finite group global and gauged $q$-form symmetries into the axiomatic structure of $d$-dimensional Topological Quantum Field Theory (TQFT) in terms of bordisms decorated by cohomology classes. Namely, on a…

This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a…

We prove rigidity facts for groups acting on pseudo-Riemannian manifolds by preserving unparameterized geodesics.

In this series of two articles, we prove that every action of a finite group $G$ on a finite and contractible $2$-complex has a fixed point. The proof goes by constructing a nontrivial representation of the fundamental group of each of the…

In this article, when G is a locally compact quantum group, we associate to a braided-commutative G-Yetter-Drinfel'd algebra $(N,a,\hat{a})$ equipped with a normal faithful semi-finite weight verifying some appropriate condition, a…