6 papers · 1 filter
Hyperbolic Knots and Torsion in Khovanov Homology
Micah Chrisman, Sujoy Mukherjee
In this note, we show that if there is a knot in having torsion in its Khovanov homology, then there are infinitely many hyperbolic knots and infinitely many p…
Arbitrarily large torsion in Khovanov cohomology
Sujoy Mukherjee, Dirk Schuetz
For any positive integer and we construct a link which has a direct summand in its Khovanov cohomology.
On odd torsion in even Khovanov homology
Sujoy Mukherjee
This short note resolves the most important part of the PS braid conjecture while introducing the first known examples of knots and links with odd torsion of order 9, 27, 81, and 2…
Schur Multipliers and Second Quandle Homology
Rhea Palak Bakshi, Dionne Ibarra, Sujoy Mukherjee +2
We define a map from second quandle homology to the Schur multiplier and examine its properties. Furthermore, we express the second homology of Alexander quandles in terms of exter…
On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere
Rhea Palak Bakshi, Sujoy Mukherjee, Józef H. Przytycki +2
Based on the presentation of the Kauffman bracket skein module of the torus given by the third author in previous work, Charles D. Frohman and Răzvan Gelca established a complete d…
On the rack homology of graphic quandles
Sujoy Mukherjee, Józef H. Przytycki
This paper has partially a novel and partially a survey character. We start with a short review of rack (two term) homology of self distributive algebraic structures (shelves) and…