10 citations · 43 across the 21 of their papers we have counts for
24 papers
Connected components of the topological surgery graph of a unicellular collection
Nick Salter, Abdoul Karim Sane
A unicellular collection on a surface is a collection of curves whose complement is a single disk. There is a natural surgery operation on unicellular collections, endowing the set…
Generating the homology of covers of surfaces
Marco Boggi, Andrew Putman, Nick Salter
Putman and Wieland conjectured that if is a finite branched cover between closed oriented surfaces of sufficiently high genus, then the orbits of all nonzer…
Stratified braid groups: monodromy
Nick Salter
The space of monic squarefree complex polynomials has a stratification according to the multiplicities of the critical points. We introduce a method to study these strata by way of…
Holomorphic maps between configuration spaces of Riemann surfaces
Lei Chen, Nick Salter
We prove a suite of results classifying holomorphic maps between configuration spaces of Riemann surfaces; we consider both the ordered and unordered setting as well as the cases o…
Totally symmetric sets in the general linear group
Noah Caplinger, Nick Salter
A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homom…
Simple closed curves in stable covers of surfaces
Nick Salter
Let be a regular covering of a surface of finite type with nonempty boundary, with finitely-generated (possibly infinite) deck group . We give necessary and suf…
Surface bundles and the section conjecture
Wanlin Li, Daniel Litt, Nick Salter +1
We formulate a tropical analogue of Grothendieck's section conjecture: that for every stable graph G of genus g>2, and every field k, the generic curve with reduction type G over k…
Vanishing cycles, plane curve singularities, and framed mapping class groups
Pablo Portilla Cuadrado, Nick Salter
Let f be an isolated plane curve singularity with Milnor fiber of genus at least 5. For all such f, we give (a) an intrinsic description of the geometric monodromy group that does…
Global fixed points of mapping class group actions and a theorem of Markovic
Lei Chen, Nick Salter
We give a short and elementary proof of the non-realizability of the mapping class group via homeomorphisms. This was originally established by Markovic, resolving a conjecture of…
Framed mapping class groups and the monodromy of strata of Abelian differentials
Aaron Calderon, Nick Salter
This paper investigates the relationship between strata of abelian differentials and various mapping class groups afforded by means of the topological monodromy representation. Bui…
Relative homological representations of framed mapping class groups
Aaron Calderon, Nick Salter
Let be a surface with either boundary or marked points, equipped with an arbitrary framing. In this note we determine the action of the associated "framed mapping class group"…
Higher spin mapping class groups and strata of Abelian differentials over Teichm{ü}ller space
Aaron Calderon, Nick Salter
For , we give a complete classification of the connected components of strata of abelian differentials over Teichmüller space, establishing an analogue of Kontsevich and Z…
Linear-central filtrations and the image of the Burau representation
Nick Salter
The Burau representation is a fundamental bridge between the braid group and diverse other topics in mathematics. A 1974 question of Birman asks for a description of the image; in…
Section problems for configurations of points on the Riemann sphere
Lei Chen, Nick Salter
This paper contains a suite of results concerning the problem of adding distinct new points to a configuration of distinct points on the Riemann sphere, such that the new p…
Arithmeticity of the monodromy of some Kodaira fibrations
Nick Salter, Bena Tshishiku
A question of Griffiths-Schmid asks when the monodromy group of an algebraic family of complex varieties is arithmetic. We resolve this in the affirmative for the class of algebrai…
The Birman exact sequence does not virtually split
Lei Chen, Nick Salter
This paper answers a basic question about the Birman exact sequence in the theory of mapping class groups. We prove that the Birman exact sequence does not admit a section over any…
Monodromy and vanishing cycles in toric surfaces
Nick Salter
Given an ample line bundle on a toric surface, a question of Donaldson asks which simple closed curves can be vanishing cycles for nodal degenerations of smooth curves in the compl…
On the monodromy group of the family of smooth plane curves
Nick Salter
We consider the space of smooth complex projective plane curves of degree d. Defined over this is the tautological family of plane curves, and hence there is a monodromy representa…
Cup products in surface bundles, higher Johnson invariants, and MMM classes
Nick Salter
In this paper we prove a family of results connecting the problem of computing cup products in surface bundles to various other objects that appear in the theory of the cohomology…
On the non-realizability of braid groups by diffeomorphisms
Nick Salter, Bena Tshishiku
For every compact surface of finite type (possibly with boundary components but without punctures), we show that when is sufficiently large there is no lift of the surf…
Surface bundles over surfaces with arbitrarily many fiberings
Nick Salter
In this paper we give the first example of a surface bundle over a surface with at least three fiberings. In fact, for each we construct -manifolds admitting at le…
Sandpiles and Dominos
Laura Florescu, Daniela Morar, David Perkinson +2
We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axe…
Cup products, the Johnson homomorphism, and surface bundles over surfaces with multiple fiberings
Nick Salter
Let be a surface bundle over a surface with monodromy representation contained in the Torelli group . In…
A Note on the Critical Group of a Line Graph
David Perkinson, Nicholas Salter, Tianyuan Xu
This note answers a question posed by Levine in arkiv:math.CO/0906.2809. The main result is Theorem 1 which shows that under certain circumstances a critical group of a directed gr…