A. Beliakova

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math.GT2025

Quantum Invariants of Ribbon Surfaces in $4$ -Dimensional $2$ -Handlebodies

Anna Beliakova, Marco De Renzi, Quentin Faes

We use unimodular ribbon categories to construct quantum invariants of ribbon surfaces in $4$ -dimensional $2$ -handlebodies up to $1$ -isotopy. In the process, we recover invariants…

math.GT2025

Algebraic Presentation of $4$ -Dimensional $2$ -Handlebodies and $3$ -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 $3 Cob$ and $4\ma…

math.GT2025

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…

math.GT2024

Abelian TQFTS and SchrÃ¶dinger local systems

Aleksei Andreev, Anna Beliakova, Christian Blanchet

We construct an action of 3-cobordisms on the finite dimensional SchrÃ¶dinger representations of the Heisenberg group by Lagrangian correspondences. In addition, we review the cons…

Quantum Invariants of Ribbon Surfaces in 4-Dimensional 2-Handlebodies

Algebraic Presentation of 4-Dimensional 2-Handlebodies and 3-Dimensional Cobordisms

A proof of Dunfield-Gukov-Rasmussen Conjecture

Abelian TQFTS and SchrÃ¶dinger local systems

Quantum Invariants of Ribbon Surfaces in $4$ -Dimensional $2$ -Handlebodies

Algebraic Presentation of $4$ -Dimensional $2$ -Handlebodies and $3$ -Dimensional Cobordisms