Anastasiia Tsvietkova

Simplicial volume of links from link diagrams

The hyperbolic volume of a link complement is known to be unchanged when a half-twist is added to a link diagram, and a suitable 3-punctured sphere is present in the complement. We generalize this to the simplicial volume of link complements by analyzing the corresponding toroidal decompositions. We then use it to prove a refined upper bound for the volume in terms of twists of various lengths for links.

The Number of Surfaces of Fixed Genus in an Alternating Link Complement

Let

An alternative approach to hyperbolic structures on link complements

L

A REFINED UPPER BOUND FOR THE HYPERBOLIC VOLUME OF ALTERNATING LINKS AND THE COLORED JONES POLYNOMIAL

be a prime alternating link with

Decomposition of Cellular Balleans

n

Exact volume of hyperbolic 2-bridge links

crossings. We show that for each fixed

Hyperbolic Structures from Link Diagrams

g

Intercusp geodesics and the invariant trace field of hyperbolic 3-manifolds

, the number of genus

Determining isotopy classes of crossing arcs in alternating links

g

NP-hard problems naturally arising in knot theory

incompressible surfaces in the complement of