2 citations · 2 across the 6 of their papers we have counts for
7 papers
Lens space surgeries on knots of small genus
Misha Schmalian, Steven Sivek
We prove that the pretzel knot is the only hyperbolic knot of genus at most with a lens space surgery. Our key technical result asserts that if a genus- hyperboli…
Links have no characterising slopes
Marc Kegel, Misha Schmalian
We show that there is no analogue of characterising slopes for multi-component links. Concretely, we show that for any ordered link L in S3 with n>1 components and any rational slo…
Unique Surgery Descriptions along Knots
Marc Kegel, Misha Schmalian
We prove that for any non-trivial knot K, infinitely many r-surgeries K(r) along K have a unique surgery description along a knot. Moreover, we show that for any hyperbolic L-space…
An algorithm for finding minimal volume hyperbolic links and the Dehn parental test
Misha Schmalian
We describe an algorithm that, given a 3-manifold M, outputs a finite set containing all minimal volume k-component hyperbolic link complements in M. A key step, that might be of i…
Cusp shape and fractional Dehn twists of fibred hyperbolic 3-manifolds
Misha Schmalian
Given a fibred hyperbolic 3-manifold with boundary, we coarsely relate the Euclidean geometry of its cusps to the classical fractional Dehn twist coefficient of its monodromy. This…
Obstructing Anosov flows on cusped 3-manifolds
Misha Schmalian
Using results relating taut foliations and pseudo-Anosov flows, we find cusped hyperbolic 3-manifolds which are not the non-singular part of a pseudo-Anosov flow. In particular, we…
How one can repair non-integrable Kahan discretizations. II. A planar system with invariant curves of degree 6
Misha Schmalian, Yuri B. Suris, Yuriy Tumarkin
We find a novel one-parameter family of integrable quadratic Cremona maps of the plane preserving a pencil of curves of degree 6 and of genus 1. They turn out to serve as Kahan-typ…