Kevin Kordek

activity

20152021

most citedHomomorphisms of commutator subgroups of braid groups

13 citations · 30 across the 5 of their papers we have counts for

collaborators

11 papers

math.GR2021★ 3 cited

Upper Bounds for Totally Symmetric Sets

Kevin Kordek, Qiao Li, Caleb Partin

Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain fa…

math.GT2020★ 5 cited

Small Quotients of Braid Groups

Noah Caplinger, Kevin Kordek

We prove that the symmetric group $S_{n}$ is the smallest non-cyclic quotient of the braid group $B_{n}$ for $n = 5, 6$ and that the alternating group $A_{n}$ is the smallest non-trivial qu…

math.GT2019

Finite quotients of braid groups

Alice Chudnovsky, Kevin Kordek, Qiao Li +1

We derive a lower bound on the size of finite non-cyclic quotients of the braid group that is superexponential in the number of strands. We also derive a similar lower bound for no…

math.GT2019

The commutator subgroup of the braid group is generated by two elements

Kevin Kordek

For $n$ at least 7 and $n$ equal to 5, we give generating sets of size 2 for the commutator subgroup of the braid group on $n$ strands. These generating sets are of the smallest po…

math.GT2019★ 13 cited

Homomorphisms of commutator subgroups of braid groups

Kevin Kordek, Dan Margalit

We give a complete classification of homomorphisms from the commutator subgroup of the braid group on $n$ strands to the braid group on $n$ strands when $n$ is at least 7. In parti…

math.GT2019★ 9 cited

Homomorphisms between braid groups

Lei Chen, Kevin Kordek, Dan Margalit

We give a complete classification of homomorphisms from the braid group on $n$ strands to the braid group on $2 n$ strands when $n$ is at least 5. We also classify endomorphisms of…

math.GT2019

Representation stability in the level 4 braid group

Kevin Kordek, Dan Margalit

We investigate the cohomology of the level 4 subgroup of the braid group, namely, the kernel of the mod 4 reduction of the Burau representation at $t = - 1$ . This group is also equal…

math.AG2016

Picard groups of moduli spaces of curves with symmetry

Kevin Kordek

We study the Picard groups of moduli spaces of smooth complex projective curves that have a group of automorphisms with a prescribed topological action. One of our main tools is th…

math.GT2015

Finiteness properties of the Johnson subgroups

Kevin Kordek

The main goal of this note is to provide evidence that the first rational homology of the Johnson subgroup $K_{g, 1}$ of the mapping class group of a genus g surface with one marked…

math.AG2015

The infinite topology of the hyperelliptic locus in Torelli space

Kevin Kordek

Genus $g$ Torelli space is the moduli space of genus $g$ curves of compact type equipped with a homology framing. The hyperelliptic locus is a closed analytic subvariety consisting…

math.AG2015

The topology of the zero locus of a genus 2 theta function

Kevin Kordek

Mess showed that the genus 2 Torelli group $T_{2}$ is isomorphic to a free group of countably infinite rank by showing that genus 2 Torelli space is homotopy equivalent to an infinit…