3 papers
math.GT2026
Maximal universal invariants from finite quotients of Verma modules
Cristina Ana-Maria Anghel, Jun Murakami
We construct a sequence of new universal quantum knot invariants that are lifts of both the semi-simple and non semi-simple quantum knot invariants. More specifically,…
math.GT2025
Complexified tetrahedrons, fundamental groups, and volume conjecture for double twist knots
Jun Murakami
In this paper, the volume conjecture for double twist knots are proved. The main tool is the complexified tetrahedron and the associated representation…
math.GT2024
Quantum fundamental group of knot and its representation
Jun Murakami, Roland van der Veen
The theory of bottom tangles is used to construct a quantum fundamental group. On the other hand, the skein module is considered as a quantum analogue of the representation…