6 papers
Motion groups, Legendrian links, and non-trivial loops of embeddings
Gabriel Corrigan, Isacco Nonino
We introduce, for an embedded Legendrian link~ in a contact 3-manifold~, the group of its \emph{Legendrian motions}. Analogously with the smooth case, we prove that this…
Khovanov monodromy groups via motions
Gabriel Corrigan, Livio Ferretti, Isacco Nonino +1
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{unorient…
A survey on mapping class groups of 3-manifolds
Philipp Bader, Rachael Boyd, Giulia Carfora +8
We survey computations and tools concerning the mapping class group of a compact, oriented, connected 3-manifold . We provide a guide to the literature and sketch proofs for var…
Outer space and finiteness properties for symmetric automorphisms of RAAGs, and generalisations
Gabriel Corrigan
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 comple…
Realising VCD for untwisted automorphism groups of RAAGs
Gabriel Corrigan
The virtual cohomological dimension of~ is given precisely by the dimension of the spine of Culler--Vogtmann Outer space. However, the dimension of the spi…
Universality for tropical and logarithmic maps
Gabriel Corrigan, Navid Nabijou, Dan Simms
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 sin…