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Christopher J Leininger

Publications and source records attributed to Christopher J Leininger.

9 recordsLinked to original sources
arXiv2021

A universal Cannon-Thurston map and the surviving curve complex

Using the Birmanexact sequence for pure mapping class groups, we construct a universal Cannon--Thurston map onto the boundary of a curve complex for a surface with punctures we call surviving curve complex. Along the way we prove hyperbolicity of this complex and identify its boundary as a space of laminations. As a corollary we obtain a universal Cannon--Thurston map to the boundary of the ordinary curve complex, extending earlier work of the second author with Mj and Schleimer.

math.GT↗
arXiv2020

Cylinder curves in finite holonomy flat metrics

For an orientable surface of finite type equipped with a flat metric with holonomy of finite order q, the set of maximal embedded cylinders can be empty, non-empty, finite, or infinite. The case when q < 3 is well-studied as such surfaces are (semi-)translation surfaces. Not only is the set always infinite, the core curves form an infinite diameter subset of the curve complex. In this paper we focus on the case q > 2 and construct examples illustrating a range of behaviors for the embedded cylinder curves. We prove that if q > 2 and the surface is fully punctured, then the embedded cylinder curves form a finite diameter subset of the curve complex. The same analysis shows that the embedded cylinder curves can only have infinite diameter when the metric has a very specific form. Using this we characterize precisely when the embedded cylinder curves accumulate on a point in the Gromov boundary.

math.GT↗
arXiv2017

Strict contractions and exotic SO_0(d,1) quotients

For d < 5, we describe an elementary construction of nonzero degree, strict contractions between closed, oriented hyperbolic d-oribifolds. Appealing to work of Gueritaud-Kassel and Tholozan, these examples determine exotic quotients of SO_0(d,1).

math.GT↗
arXiv2015

An arc graph distance formula for the flip graph

Using existing technology, we prove a Masur-Minsky style distance formula for flip- graph distance between two triangulations, expressed as a sum of the distances of the projections of these triangulations into arc graphs of the suitable subsurfaces of S.

math.GT↗
arXiv2014

Unbounded asymmetry of stretch factors

A result of Handel-Mosher guarantees that the ratio of logarithms of stretch factors of any fully irreducible automorphism of the free group $F_N$ and its inverse is bounded by a constant $C_N$. In this short note we show that this constant $C_N$ cannot be chosen independent of $N$.

math.GR↗
arXiv2009

Simon's conjecture for fibered knots

The main result of this paper, Simon's conjecture for fibered knots, was previously proven by Silver and Whitten math.GT/0405462 with essentially the same proof. This paper is therefore being withdrawn. The author would like to apologize for having missed this.

math.GT↗
arXiv2008

Two-generator subgroups of the pure braid group

We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group actions on trees.

math.GT↗
arXiv2007

Uniform convergence in the mapping class group

We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit sets, but are not convex cocompact.

math.GT↗