PreprintCC BY 4.0HAL
Triple-cup product forms of 3-manifolds and Heegaard diagrams
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.
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BibTeX
@misc{kayali2026triplecup,
title = {{Triple-cup product forms of 3-manifolds and Heegaard diagrams}},
author = {Maya Kayali},
howpublished = {HAL},
year = {2026},
month = oct,
eprint = {2604.13999},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05820737v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Triple-cup product forms of 3-manifolds and Heegaard diagrams
AU - Maya Kayali
PY - 2026
DA - 2026/10/13
PB - HAL
UR - https://hal.science/hal-05820737v1
AB - 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.
ER -