181 citations · 551 across the 67 of their papers we have counts for
13 papers · 1 filter
Kauffman bracket skein modules of small 3-manifolds
Renaud Detcherry, Efstratia Kalfagianni, Adam S. Sikora
The proof of Witten's finiteness conjecture established that the Kauffman bracket skein modules of closed -manifolds are finitely generated over . In this paper, w…
Adequate links in thickened surfaces and the generalized Tait conjectures
Hans U. Boden, Homayun Karimi, Adam S. Sikora
In this paper, we apply Kauffman bracket skein algebras to develop a theory of skein adequate links in thickened surfaces. We show that any alternating link diagram on a surface is…
Tangle Equations, the Jones conjecture, slopes of surfaces in tangle complements, and q-deformed rationals
Adam S. Sikora
We study systems of -tangle equations which play an important role in the analysis of enzyme actions on DNA strands. We show that every system of framed tangle equations has at…
Verification Of The Jones Unknot Conjecture Up To 24 Crossings
Robert E. Tuzun, Adam S. Sikora
Extending upon our previous work, we verify the Jones Unknot Conjecture for all knots up to crossings. We describe the method of our approach and analyze the growth of the com…
SU(3)-skein algebras and webs on surfaces
Charles Frohman, Adam S. Sikora
The -skein algebra of a surface is spanned by isotopy classes of certain framed graphs in called -webs subject to the skein relations encapsulating relatio…
Verification Of The Jones Unknot Conjecture Up To 23 Crossings
Robert E. Tuzun, Adam S. Sikora
The Jones unknot conjecture states that the Jones polynomial distinguishes the unknot from nontrivial knots. We prove it for knots up to 23 crossings.