Cyclic Objects from Surfaces

Q: What type of study is this?

This is a Quantitative Study study.

Ivan Bartulović

doi:10.3842/sigma.2025.074

September 6, 2025Symmetry Integrability and Geometry Methods and ApplicationsOpen Access

Cyclic Objects from Surfaces

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Key Points

Any closed genus surface can be structured as a (co)cyclic object in 3-dimensional cobordisms, enhancing its mathematical framework.
The framework leads to new algebraic computations for modules induced by 3-dimensional TQFTs, specifically for the Reshetikhin-Turaev TQFT.
This approach offers a novel perspective on TQFTs, revealing deeper connections to algebraic structures in topology.
Utilizing (co)cyclic structures can inform the understanding of relationships between various topological invariants.

Implication

This research presents (co)cyclic structures on closed genus surfaces, suggesting new ties to 3-dimensional TQFTs.

Abstract

In this paper, we endow the family of all closed genus g ≥ 1 surfaces with a structure of a (co)cyclic object in the category of 3-dimensional cobordisms. As a corollary, any $3$-dimensional TQFT induces a (co)cyclic module, which we compute algebraically for the Reshetikhin-Turaev TQFT.

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Cite This Study

Ivan Bartulović (2025) studied this question.

synapsesocial.com/papers/68d4566c31b076d99fa5ba42 https://doi.org/10.3842/sigma.2025.074

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Cyclic Objects from Surfaces

Key Points

Implication

Abstract

Discussion

Cite This Study

Cyclic Objects from Surfaces

Key Points

Implication

Abstract

Discussion

Cite This Study

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