arXiv research

(1,1) non-L-space knots are foliar in 3D space.

A knot $κ$ in $S^3$ is persistently foliar if, for each non-trivial boundary slope, there is a co-oriented taut foliation meeting the boundary of the knot complement transversely in a foliation by curves of that slope. For rational slopes, these foliations may be capped off by disks to obtain a co-oriented taut foliati…

A 3-manifold is foliar if it supports a codimension-one co-oriented taut foliation. Suppose $M$ is an oriented 3-manifold with connected boundary a torus, and suppose $M$ contains a properly embedded, compact, oriented, surface $R$ with a single boundary component that is Thurston norm minimizing in $H_2(M, \partial M)…

The study proves knots and certain links support taut foliations.

This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, and admitting a co-orientable taut foliation. In particular, it adds further evidence in favor of this conjecture by studying these t…

Availability of an explainable deep learning model that can be applied to practical real world scenarios and in turn, can consistently, rapidly and accurately identify specific and minute traits in applicable fields of biological sciences, is scarce. Here we consider one such real world example viz., accurate identific…

Classifies $L$-space surgeries on all two-bridge links