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Triple-cup product forms of 3-manifolds and Heegaard diagrams

Year: 2026

Type: article

Abstract: The triple-cup product form 𝜇 is a classical invariant of 3-manifolds, determining the cohomology ring up to torsion.Given a closed, connected, oriented 3-manifold 𝑀, we describe an explicit formula for computing 𝜇 from a Heegaard diagram of 𝑀.Then, we show that the triple-cup product form 𝜇 can be recovered as a reduction of Turaev's homotopy intersection form 𝜂 of the Heegaard surface.

Source: Canadian Journal of Mathematics

DOI: 10.4153/s0008414x26102661

Author: Maya Kayali

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W7154593732

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