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arXiv · 2205.14706

Simple balanced three-manifolds, Heegaard Floer homology and the Andrews-Curtis conjecture

Neda Bagherifard·Eaman Eftekhary
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Abstract

The first author introduced a notion of equivalence on a family of $3$-manifolds with boundary, called (simple) balanced $3$-manifolds in an earlier paper and discussed the analogy between the Andrews-Curtis equivalence for group presentations and the aforementioned notion of equivalence. Motivated by the Andrews-Curtis conjecture, we use tools from Heegaard Floer theory to prove that there are simple balanced $3$-manifolds which are not in the trivial equivalence class (i.e. the equivalence class of $S^2\times [-1,1]$).

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Neda Bagherifard, Eaman Eftekhary. 2022-06-02. Simple balanced three-manifolds, Heegaard Floer homology and the Andrews-Curtis conjecture. https://doi.org/10.2140/agt.2024.24.4519

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