26 citations · 180 across the 37 of their papers we have counts for
18 papers · 1 filter
Quantum Invariants of Ribbon Surfaces in -Dimensional -Handlebodies
Anna Beliakova, Marco De Renzi, Quentin Faes
We use unimodular ribbon categories to construct quantum invariants of ribbon surfaces in -dimensional -handlebodies up to -isotopy. In the process, we recover invariants…
Algebraic Presentation of -Dimensional -Handlebodies and -Dimensional Cobordisms
Anna Beliakova, Ivelina Bobtcheva, Marco De Renzi +1
In this paper, we give a new direct proof of a result by Bobtcheva and Piergallini that provides finite algebraic presentations of two categories, denoted and $4\ma…
Abelian TQFTS and Schrödinger local systems
Aleksei Andreev, Anna Beliakova, Christian Blanchet
We construct an action of 3-cobordisms on the finite dimensional Schrödinger representations of the Heisenberg group by Lagrangian correspondences. In addition, we review the const…
On unification of colored annular sl(2) knot homology
Anna Beliakova, Matthew Hogancamp, Krzysztof Karol Putyra +1
We show that the Khovanov and Cooper-Krushkal models for colored sl(2) homology are equivalent in the case of the unknot, when formulated in the quantum annular Bar-Natan category.…
A proof of Dunfield-Gukov-Rasmussen Conjecture
Anna Beliakova, Krzysztof K. Putyra, Louis-Hadrien Robert +1
In 2005 Dunfield, Gukov and Rasmussen conjectured an existence of the spectral sequence from the reduced triply graded Khovanov-Rozansky homology of a knot to its knot Floer homolo…
Refined Bobtcheva-Messia Invariants of 4-Dimensional 2-Handlebodies
Anna Beliakova, Marco De Renzi
In this paper we refine our recently constructed invariants of -dimensional -handlebodies up to -deformations. More precisely, we define invariants of pairs of the form $(…
Algebraic versus geometric categorification of the~Alexander polynomial: a~spectral sequence
Krzysztof K Putyra, Anna Beliakova, Louis-Hadrien Robert +1
We construct a bigraded spectral sequence from the gl(0)-homology to knot Floer homology. This spectral sequence is of Bockstein type and comes from a subtle manipulation of coeffi…
Kerler-Lyubashenko Functors on 4-Dimensional 2-Handlebodies
Anna Beliakova, Marco De Renzi
We construct a braided monoidal functor from Bobtcheva and Piergallini's category of connected 4-dimensional 2-handlebodies (up to 2-deformations) to an arbitr…
Non-semisimple invariants and Habiro's series
Anna Beliakova, Kazuhiro Hikami
In this paper we establish an explicit relationship between Habiro's cyclotomic expansion of the colored Jones polynomial (evaluated at a p-th root of unity) and the Akutsu-Deguchi…
Logarithmic Hennings invariants for restricted quantum sl(2)
Anna Beliakova, Christian Blanchet, Nathan Geer
We construct a Hennings type logarithmic invariant for restricted quantum at a -th root of unity. This quantum group is not braided, but factori…
Quantum Link Homology via Trace Functor I
Anna Beliakova, Krzysztof Karol Putyra, Stephan Martin Wehrli
Motivated by topology, we develop a general theory of traces and shadows for an endobicategory, which is a~pair: bicategory and endobifunctor $Σ\colon \mathbf C \to\ma…
On the unification of quantum 3-manifold invariants
Anna Beliakova, Thang Le
In 2006 Habiro initiated a construction of generating functions for Witten-Reshetikhin-Turaev (WRT) invariants known as unified WRT invariants. In a series of papers together with…
On Link Homology Theories from Extended Cobordisms
Anna Beliakova, Emmanuel Wagner
This paper is devoted to the study of algebraic structures leading to link homology theories. The originally used structures of Frobenius algebra and/or TQFT are modified in two di…
A Unified Quantum SO(3) Invariant for Rational Homology 3-Spheres
Anna Beliakova, Irmgard Buehler, Thang Le
Given a rational homology 3-sphere M with the first integral homology of rank b and a link L inside M, colored by odd numbers, we construct a unified invariant I_{M,L} belonging to…
A Simplification of Combinatorial Link Floer Homology
Anna Beliakova
We define a new combinatorial complex computing the hat version of link Floer homology over Z/2Z, which turns out to be significantly smaller than the Manolescu-Ozsvath-Sarkar one.
Integrality of quantum 3-manifold invariants and rational surgery formula
Anna Beliakova, Thang T. Q. Le
We prove that the Witten-Reshetikhin-Turaev (WRT) SO(3) invariant of an arbitrary 3-manifold M is always an algebraic integer. Moreover, we give a rational surgery formula for the…
Rational surgery formula for Habiro-Le invariants of rational homology 3-spheres
Anna Beliakova
The results become part of an upcoming paper.
Refined invariants and TQFT's from Homfly skein theory
Anna Beliakova
We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed orien…