arXiv subjects

Chris Grossack

Publications and source records attributed to Chris Grossack.

3 recordsLinked to original sources

arXiv2025

Explicitly Computing with Fukaya Categories of Surfaces with Boundary

Fukaya categories are deep and rich invariants of symplectic manifolds which are notoriously difficult to compute explicitly. In the case of surfaces, however, the situation is simple, combinatorial,and is very well understood (at least by experts). In this expository paper we will give an introduction with many examples to welcome newcomers to the area and hopefully equip them with the tools to independently compute Fukaya categories of surfaces.

math.SG↗

arXiv2023

The Right Angled Artin Group Functor as a Categorical Embedding

It has long been known that the combinatorial properties of a graph $\Gamma$ are closely related to the group theoretic properties of its right angled artin group (raag). It's natural to ask if the graph homomorphisms are similarly related to the group homomorphisms between two raags. The main result of this paper shows that there is a purely algebraic way to characterize the raags amongst groups, and the graph homomorphisms amongst the group homomorphisms. As a corollary we present a new algorithm for recovering $\Gamma$ from its raag.

math.GR↗

arXiv2020

Extensions of Abelian Automata Groups

A theorem of Nekrashevych and Sidki shows the Mealy Automata structures one can place on Z^m are parametrized by a family of matrices (called "1/2-integral") and a choice of residuation vector e in Z^m. While the impact of the chosen matrix is well understood, the impact of the residuation vector on the resulting structure is seemingly sporadic. In this paper we characterize the impact of the residuation vector e by recognizing an initial structure when e is the first standard basis vector. All other choices of e extend this initial structure by adding "fractional elements" in a way we make precise.

cs.FL↗