15 citations · 85 across the 24 of their papers we have counts for
25 papers
Action of subgroups of the mapping class group on Heisenberg homologies
Christian Blanchet, Martin Palmer, Awais Shaukat
In previous work we constructed twisted representations of mapping class groups of surfaces, depending on a choice of representation of the Heisenberg group . For…
Polynomiality of surface braid and mapping class group representations
Martin Palmer, Arthur Soulié
We study a wide range of homologically-defined representations of surface braid groups and of mapping class groups of surfaces, including the Lawrence-Bigelow representations of th…
Big mapping class groups with uncountable integral homology
Martin Palmer, Xiaolei Wu
We prove that, for any infinite-type surface , the integral homology of the closure of the compactly-supported mapping class group and of the Tor…
Homology stability for asymptotic monopole moduli spaces
Martin Palmer, Ulrike Tillmann
We prove homological stability for two different flavours of asymptotic monopole moduli spaces, namely moduli spaces of framed Dirac monopoles and moduli spaces of ideal monopoles.…
On the homology of big mapping class groups
Martin Palmer, Xiaolei Wu
We prove that the mapping class group of the one-holed Cantor tree surface is acyclic. This in turn determines the homology of the mapping class group of the once-punctured Cantor…
The pro-nilpotent Lawrence-Krammer-Bigelow representation
Martin Palmer, Arthur Soulié
We construct a 3-variable enrichment of the Lawrence-Krammer-Bigelow (LKB) representation of the braid groups, which is the limit of a pro-nilpotent tower of representations having…
When the lower central series stops: a comprehensive study for braid groups and their relatives
Jacques Darné, Martin Palmer, Arthur Soulié
Understanding the lower central series of a group is, in general, a difficult task. It is, however, a rewarding one: computing the lower central series and the associated Lie algeb…
The Burau representations of loop braid groups
Martin Palmer, Arthur Soulié
We give a simple topological construction of the Burau representations of the loop braid groups. There are four versions: defined either on the non-extended or extended loop braid…
Heisenberg homology on surface configurations
Christian Blanchet, Martin Palmer, Awais Shaukat
Motivated by the Lawrence-Krammer-Bigelow representations of the classical braid groups, we study the homology of unordered configurations in an orientable genus- surface with o…
Lawrence-Bigelow representations, bases and duality
Cristina Ana-Maria Anghel, Martin Palmer
We study homological representations of mapping class groups, including the braid groups. These arise from the twisted homology of certain configuration spaces, and come in many di…
Motivic homological stability of configuration spaces
Geoffroy Horel, Martin Palmer
We prove that some of the classical homological stability results for configuration spaces of points in manifolds can be lifted to motivic cohomology.
Point-pushing actions for manifolds with boundary
Martin Palmer, Ulrike Tillmann
Given a manifold and a point in its interior, the point-pushing map describes a diffeomorphism that pushes the point along a closed path. This defines a homomorphism from the f…
Configuration-mapping spaces and homology stability
Martin Palmer, Ulrike Tillmann
For a given bundle over a manifold, configuration-section spaces on parametrise finite subsets equipped with a section of defined on $M \s…
Lectures on invertible field theories
Arun Debray, Soren Galatius, Martin Palmer
Four lectures on invertible field theories at the Park City Mathematics Institute 2019. Cobordism categories are introduced both as plain categories and topologically enriched. We…
Topological representations of motion groups and mapping class groups -- a unified functorial construction
Martin Palmer, Arthur Soulié
For groups of a topological origin, such as braid groups and mapping class groups, an important source of interesting and highly non-trivial representations is given by their actio…
Advanced topics in gauge theory: mathematics and physics of Higgs bundles
Laura P. Schaposnik
These notes have been prepared as reading material for the mini-course given by the author at the "2019 Graduate Summer School" at Park City Mathematics Institute - Institute for A…
Stability for moduli spaces of manifolds with conical singularities
Martin Palmer
The homology of configuration spaces of point-particles in manifolds has been studied intensively since the 1970s; in particular it is known to be stable if the underlying manifold…
Homological stability for moduli spaces of disconnected submanifolds, I
Martin Palmer
A well-known property of unordered configuration spaces of points (in an open, connected manifold) is that their homology stabilises as the number of points increases. We generalis…
A comparison of twisted coefficient systems
Martin Palmer
In the first part of this note, we review and compare various instances of the notion of twisted coefficient system, a.k.a. polynomial functor, appearing in the literature. This no…
Triple-crossing number and moves on triple-crossing link diagrams
Colin Adams, Jim Hoste, Martin Palmer
Every link in the 3-sphere has a projection to the plane where the only singularities are pairwise transverse triple points. The associated diagram, with height information at each…
A twisted homology fibration criterion and the twisted group-completion theorem
Jeremy Miller, Martin Palmer
The purpose of this note is to clarify some details in McDuff and Segal's proof of the group-completion theorem and to generalize both this and the homology fibration criterion of…
On homological stability for configuration spaces on closed background manifolds
Federico Cantero, Martin Palmer
We introduce a new map between configuration spaces of points in a background manifold - the replication map - and prove that it is a homology isomorphism in a range with certain c…
Twisted homological stability for configuration spaces
Martin Palmer
Let M be an open, connected manifold. A classical theorem of McDuff and Segal states that the sequence of configuration spaces of n unordered, distinct points in M is homologically…
Scanning for oriented configuration spaces
Jeremy Miller, Martin Palmer
In [Pal13] (arXiv:1106.4540) the second author proved that the sequence of "oriented" configuration spaces on an open connected manifold exhibits homological stability as the numbe…