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

Bagherifard, Neda; Eftekhary, Eaman

doi:10.2140/agt.2024.24.4519

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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

DOI: 10.2140/agt.2024.24.4519

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 $S^{2} \times [- 1, 1]$ ).

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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Volume 24, issue 8 (2024)