arXiv subjects

Gabriel Corrigan

Publications and source records attributed to Gabriel Corrigan.

5 recordsLinked to original sources

arXiv2026

Khovanov monodromy groups via motions

For any link, we define a monodromy map from the motion group of the link to the group of automorphisms of the link's Khovanov homology. The image of this map is the \emph{unoriented monodromy group} of the link. This map allows us to convert results concerning motion groups of links into ones about their Khovanov monodromy. In particular, we use a characterisation of the motion groups of split links to write their unoriented monodromy groups as an explicit semidirect product in terms of their unsplit pieces. We give some demonstrative examples, computing the unoriented monodromy groups of unlinks, Hopf links, and split links composed of pieces thereof.

math.GT↗

arXiv2026

A survey on mapping class groups of 3-manifolds

We survey computations and tools concerning the mapping class group of a compact, oriented, connected 3-manifold $M$. We provide a guide to the literature and sketch proofs for various families of irreducible and geometric 3-manifolds. We also consider JSJ and prime decompositions of 3-manifolds, and consequences for their mapping class groups.

math.GT↗

arXiv2025

Outer space and finiteness properties for symmetric automorphisms of RAAGs, and generalisations

We define the symmetric (outer) automorphism group of a right-angled Artin group and construct for it a (spine of) Outer space. This `symmetric spine' is a contractible cube complex upon which the symmetric outer automorphism group acts properly and cocompactly. One artefact of our technique is a strengthening of the proof of contractibility of the untwisted spine, mimicking the original proof that Culler--Vogtmann Outer space is contractible, which may be of independent interest. We apply our results to derive finiteness properties for certain subgroups of outer automorphisms. In particular, we prove that the subgroup consisting of those outer automorphisms which permute any given finite set of conjugacy classes of a right-angled Artin group is of type \emph{VF}, and we show that the virtual cohomological dimension of the symmetric outer automorphism group is equal to both the dimension of the symmetric spine and the rank of a free abelian subgroup.

math.GR↗

arXiv2025

Realising VCD for untwisted automorphism groups of RAAGs

The virtual cohomological dimension of~$\operatorname{Out}(F_n)$ is given precisely by the dimension of the spine of Culler--Vogtmann Outer space. However, the dimension of the spine of untwisted Outer space for a general right-angled Artin group~$A_\Gamma$ does not necessarily match the virtual cohomological dimension~$\textsc{vcd}(U(A_{\Gamma}))$ of the untwisted subgroup~$U(A_\Gamma) \leq \operatorname{Out}(A_\Gamma)$. Under certain graph-theoretic conditions, we perform an equivariant deformation retraction of this spine to produce a new contractible cube complex upon which~$U(A_\Gamma)$ acts properly and cocompactly. Furthermore, we give conditions for when the dimension of this complex realises the virtual cohomological dimension of~$U(A_\Gamma)$. We finish with two applications of our construction; in particular we show that the difference between the dimension of the untwisted spine and~$\textsc{vcd}(U(A_{\Gamma}))$ can be arbitrarily large.

math.GR↗

arXiv2022

Universality for tropical and logarithmic maps

We prove that every toric monoid appears in a space of maps from tropical curves to an orthant. It follows that spaces of logarithmic maps to Artin fans exhibit arbitrary toric singularities: a virtual universality theorem for logarithmic maps to pairs. The target rank depends on the chosen singularity: we show that the cone over the 7-gon never appears in a space of maps to a rank 1 target. We obtain similar results for tropical maps to affine space.

math.AG↗