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

Neda Bagherifard and Eaman Eftekhary

Algebraic & Geometric Topology 24 (2024) 4519–4543
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 (ie the equivalence class of S2 × [1,1]).

Keywords
Andrews–Curtis conjecture, Heegaard Floer homology, simple balanced three-manifolds
Mathematical Subject Classification
Primary: 57K18, 57R58
References
Publication
Received: 26 July 2022
Revised: 30 October 2022
Accepted: 1 February 2023
Published: 17 December 2024
Authors
Neda Bagherifard
School of Mathematics
Institute for Research in Fundamental Sciences (IPM)
Tehran
Iran
Eaman Eftekhary
School of Mathematics
Institute for Research in Fundamental Sciences (IPM)
Tehran
Iran

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