arXiv subjects

Priyadip Mondal

Publications and source records attributed to Priyadip Mondal.

5 recordsLinked to original sources

arXiv2026

One-cusped Dehn fillings of the sisters of the Whitehead and $6^2_2$ link complements

In this article, we investigate the arithmeticity of the one-cusped Dehn fillings of the $(-2,3,8)$-pretzel link complement and of the Berge manifold, which respectively are the sisters of the Whitehead and $6^2_2$ link complements. We show that for each such one-cusped hyperbolic Dehn filling, the cusp field, the trace field and the invariant trace field coincide. Moreover, we establish that no one-cusped hyperbolic Dehn filling of the Berge manifold is arithmetic and that the only arithmetic one-cusped hyperbolic Dehn filling of the $(-2,3,8)$-pretzel link complement is the sister of the figure eight knot complement. The techniques used to prove these results further show that each knot complement covering a one-cusped hyperbolic Dehn filling of either of these two sisters manifolds admits no hidden symmetries, effectively generalizing already known results in this regard.

math.GT↗

arXiv2024

Mixed-platonic 3-manifolds

We introduce a class of cusped hyperbolic $3$-manifolds that we call mixed-platonic, composed of regular ideal hyperbolic polyhedra of more than one type, which includes certain previously-known examples. We establish basic facts about mixed-platonic manifolds which allow us to conclude, among other things, that there is no mixed-platonic hyperbolic knot complement with hidden symmetries.

math.GT↗

arXiv2024

Hidden symmetries and Dehn surgery on tetrahedral links

Motivated by a question of Neumann and Reid, we study whether Dehn fillings on all but one cusp of a hyperbolic link complement can produce infinite families of knot complements with hidden symmetries which geometrically converge to the original link complement. We prove several results relating the existence of such an infinite family of knot complements with hidden symmetries to the existence of certain symmetries of the horoball packings associated to the original link. Using these results, we develop an algorithm which when run on SnapPy can test when such symmetries do not exist. We then use this SnapPy code and two utilities from \cite{orbcenpract} to show that for any given link in the tetrahedral census of Fominykh-Garoufalidis-Goerner-Tarkaev-Vesnin, no such family of Dehn fillings exists. We establish the same result for two infinite families of cyclic covers of the Berge manifold and the $6^2_2$-complement as well.

math.GT↗

arXiv2020

Dehn surgery and hyperbolic knot complements without hidden symmetries

Neumann and Reid conjecture that there are exactly three knot complements which admit hidden symmetries. This paper establishes several results that provide evidence for the conjecture. Our main technical tools provide obstructions to having infinitely many fillings of a cusped manifold produce knot complements admitting hidden symmetries. Applying these tools, we show for any two-bridge link complement, at most finitely many fillings of one cusp can be covered by knot complements admitting hidden symmetries. We also show that the figure-eight knot complement is the unique knot complement with volume less than $6v_0 \approx 6.0896496$ that admits hidden symmetries. We then conclude with two independent proofs that among hyperbolic knot complements only the figure-eight knot complement can admit hidden symmetries and cover a filling of the two-bridge link complement $\mathbb{S}^3\setminus 6^2_2$. Each of these proofs shows that the technical tools established earlier can be made effective.

math.GT↗

arXiv2019

Generic hyperbolic knot complements without hidden symmetries

We establish a pair of criteria for proving that most knot complements obtained as Dehn fillings of a given two-component hyperbolic link complement lack hidden symmetries. To do this, we use certain rational functions on varieties associated to the link. We apply our criteria to show that among certain infinite families of knot complements, all but finitely many members lack hidden symmetries.

math.GT↗