28 citations · 61 across the 12 of their papers we have counts for
14 papers
Handlebodies, Outer space, and tropical geometry
Rohini Ramadas, Rob Silversmith, Karen Vogtmann +1
The moduli space of graphs is a polyhedral object that mimics the behavior of the moduli spaces , of (stable) Riemann surfac…
Transitivity of the pure Hurwitz classes of quadratic post-critically finite polynomials
Yvon Verberne, Rebecca R. Winarski
We prove that for two post-critically finite quadratic polynomials , there is a mapping class of the sphere with finitely many marked points such that and are pur…
Thurston's theorem and the Nielsen-Thurston classification via Teichmüller's theorem
James Belk, Dan Margalit, Rebecca R. Winarski
We give a unified and self-contained proof of the Nielsen-Thurston classification theorem from the theory of mapping class groups and Thurston's characterization of rational maps f…
Twisting cubic rabbits
Justin Lanier, Rebecca R. Winarski
We solve an infinite family of twisted polynomial problems that are cubic generalizations of Hubbard's twisted rabbit problem. We show how the result of twisting by a power of a ce…
A solution to the degree-d twisted rabbit problem
Malavika Mukundan, Rebecca R. Winarski
We solve generalizations of Hubbard's twisted rabbit problem for analogues of the rabbit polynomial of degree . The twisted rabbit problem asks: when a certain quadratic p…
Pseudo-Anosov homeomorphisms of punctured non-orientable surfaces with small stretch factor
Sayantan Khan, Caleb Partin, Rebecca R. Winarski
We prove that in the non-orientable setting, the minimal stretch factor of a pseudo-Anosov homeomorphism of a surface of genus with a fixed number of punctures is asymptoticall…
Elastic Graphs for Main Molecule Matings
Caroline Davis, Jasmine Powell, Rebecca R. Winarski +1
Recent work of Dylan Thurston gives a condition for when a post-critically finite branched self-cover of the sphere is equivalent to a rational map. We apply D. Thurston's positive…
Superbridge and Bridge Indices for Knots
Colin Adams, Nikhil Agarwal, Rachel Allen +4
We improve the upper bound on the superbridge index of a knot type in terms of the bridge index from to .
Recognizing topological polynomials by lifting trees
James Belk, Justin Lanier, Dan Margalit +1
We give a simple algorithm that determines whether a given post-critically finite topological polynomial is Thurston equivalent to a polynomial. If it is, the algorithm produces th…
Big Torelli groups: generation and commensuration
Javier Aramayona, Tyrone Ghaswala, Autumn E. Kent +3
For any surface of infinite topological type, we study the Torelli subgroup of the mapping class group , whose elements are those mapping classe…
The Birman-Hilden theory
Dan Margalit, Rebecca R. Winarski
In the 1970s Joan Birman and Hugh Hilden wrote several papers on the problem of relating the mapping class group of a surface to that of a cover. We survey their work, give an over…
Lifting Homeomorphisms and Cyclic Branched Covers of Spheres
Tyrone Ghaswala, Rebecca R. Winarski
We characterize the cyclic branched covers of the 2-sphere where every homeomorphism of the sphere lifts to a homeomorphism of the covering surface. This answers a question that ap…
The liftable mapping class group of balanced superelliptic covers
Tyrone Ghaswala, Rebecca R. Winarski
The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map…
Symmetry, Isotopy, and Irregular Covers
Rebecca R. Winarski
We say that a cover of surfaces S -> X has the Birman--Hilden property if the subgroup of the mapping class group of X consisting of mapping classes that have representatives that…