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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]).
Bagherifard, Neda 1 ; Eftekhary, Eaman 1
@article{10_2140_agt_2024_24_4519,
author = {Bagherifard, Neda and Eftekhary, Eaman},
title = {Simple balanced three-manifolds, {Heegaard} {Floer} homology and the {Andrews{\textendash}Curtis} conjecture},
journal = {Algebraic and Geometric Topology},
pages = {4519--4543},
publisher = {mathdoc},
volume = {24},
number = {8},
year = {2024},
doi = {10.2140/agt.2024.24.4519},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4519/}
}
TY - JOUR AU - Bagherifard, Neda AU - Eftekhary, Eaman TI - Simple balanced three-manifolds, Heegaard Floer homology and the Andrews–Curtis conjecture JO - Algebraic and Geometric Topology PY - 2024 SP - 4519 EP - 4543 VL - 24 IS - 8 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4519/ DO - 10.2140/agt.2024.24.4519 ID - 10_2140_agt_2024_24_4519 ER -
%0 Journal Article %A Bagherifard, Neda %A Eftekhary, Eaman %T Simple balanced three-manifolds, Heegaard Floer homology and the Andrews–Curtis conjecture %J Algebraic and Geometric Topology %D 2024 %P 4519-4543 %V 24 %N 8 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4519/ %R 10.2140/agt.2024.24.4519 %F 10_2140_agt_2024_24_4519
Bagherifard, Neda; Eftekhary, Eaman. Simple balanced three-manifolds, Heegaard Floer homology and the Andrews–Curtis conjecture. Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4519-4543. doi: 10.2140/agt.2024.24.4519
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