International conference
"Quantum and classical topology of three-dimensional manifolds"
April 20 - April 22, 2015, Chelyabinsk

Conference of the laboratory of "Quantum topology" (Chelyabinsk State University), dedicated to the quantum and classical topology of three-dimensional manifolds.

Working languages​​: Russian and English

Venue: Chelyabinsk State University, first house, SRL quantum topology, aud. 430.

Organizing committee: E.A. Fominykh (head), Y.K. Ilina (secretary), E.V. Shumakova (secretary)

Program committee: V.G. Turaev (head), S.V. Matveev

The conference program:

April 20

10:00 - 10:45

V. Turaev, Matching groups and gliding systems

Abstract: With every matching in a graph we associate a group called the matching group. We study this group using the theory of non-positively curved cubed complexes. Our approach is formulated in terms of so-called gliding systems.

11:00 - 11:45

S. Matveev, Dijkgraaf-Witten invariants over Z2 for twice orientable Seifert manifolds

Abstract: Give a complete answer.

Lunch

13:00 - 13:45

E. Fominykh, On complexity of virtual manifolds

14:00 - 14:45

A. Akimova, Classification of prime genus 1 virtual knots of low complexity

Abstract: Virtual knot theory was developed by L. Kauffman in 1996. We tabulate all genus one prime virtual knots having minimal octahedron diagrams or diagrams with n < 6 classical crossings. First we construct all prime knots in the thickened torus T X I which have minimal octahedron diagrams or diagrams with n < 6 crossings and admit no destabilizations. Then we use a generalized version of the normalized Kauffman bracket to prove that all those knots are different. Finally, we convert the knot diagrams in T thus obtained into virtual knot diagrams in the plane.

15:00 - 16:00

Poster talk

A. Kulakova, A new proof of the Schubert theorem

Y. Ilyina, Casson invariant for knotoind and corresponding knots

April 21

10:00 - 10:45

A. Vesnin, A census of tetrahedral hyperbolic manifolds

Abstract: We call a cusped hyperbolic 3-manifold tetrahedral if it can be decomposed into regular ideal tetrahedra.  Simplest examples of tetrahedral manifolds are the Gieseking manifold and the figure-eight knot complement. We provide a census of all tetrahedral manifolds with at most 25 (orientable case) and 21 (non-orientable case) tetrahedra.  The talk is based on the joint paper with E. Fominykh, S. Garoufalidis, M. Goerner and V. Tarkaev (arXiv:1502.00383).

11:00 - 11:45

I. Moriah, A Normal form for highly twisted knots

Abstract: In this talk I will report on work in progress where a normal form for a large class of knots in a 2m-plat projection is presented. This normal form is a classification for these knots and is the first such classification since Schubert  classified 2-bridge knots in 1956.

Lunch

13:00 - 13:45

A. Morozov, HOMFLY polynomials for virtual knots

Abstract: In this talk we will discuss the knot invariants for the virtual knots. Although the methods of calculating SU(2) invariants were provided some time ago by L.Kauffman the much richer SU(N) invariants were unknown. The reasons for this is that the quantum group approach, used for ordinary knots breaks down due to the existence of virtual crossing.
We used recent dvances in calculating Khovanpov-Rogansky homologies to introduce another approach to the evaluting SU(N) invariants (HOMFLY polynomials) for ordinary and virtual knots. In this talk we will describe this approach and properties of  HOMFLY polynomials for virtual knots.

14:00 - 14:45

A. Masley, Gehring-Martin-Tan and Tan numbers for elementary subgroups of PSL(2,C)

Abstract: The Gehring-Martin-Tan and Tan numbers are defined for every two-generated subgroup of the group PSL(2,C). These numbers arise in necessary discreteness conditions for two-generated subgroups. We will discuss its properties and exact values for elementary subgroups.

15:00 - 16:00

Poster talk

V. Morozov, Prime decompositions of global knots

L. Nabeeva, Classification of projections and knot diagrams in thickened Klein bottle

April 22

10:00 - 10:45

R. Kashaev, Penner coordinates for closed surfaces

Abstract: We propose a version of Penner’s decorated Teichmüller space in the case of a closed surface and describe how lambda-coordinates can be used to parametrize  this space. The talk is based on the preprint arXiv:1403.0180.

11:00 - 11:45

M. Prasolov (Joint talk with Ivan Dynnikov), Annuli with Legendrian boundary

Abstract: Let A be an annulus embedded in the three-space so that A is tangent to the standard contact structure at all boundary points. This means, in particular, that A is cobounded by two knots K1, K2 that are Legendrian and have the same topological type. Is it true that K1 and K2 are always Legendrian equivalent? By using grid diagrams we prove a weaker statement and suggest a method to disprove the original one.

Lunch

13:00 - 13:45

V. Bardakov, Virtual representation of the braid group of automorphisms and virtual links

Abstract: We construct a representation from the virtual braid group VBn to the automorphism group Aut (Fn * Zn) of free product absolutely free group and a free Abelian group. Using this representation we define the group of virtual links. The proposed construction generalizes previously proposed construction of Kaufman, Manturov and Silver-Williams.

15:00 - 16:00

Poster talk

A. Nikiforov, Non-orientable Seifert manifold complexity 0

2017 Quantum topology.