Year: 2024
Type: article
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 Π1; 1).57K18, 57R58 1. Introduction 4519 2. A Heegaard diagram for the mapping torus 4523 3. Simplifying computations using algorithmic calculations 4526 4. Nonpolygonal disks with holomorphic representatives 4528 5.The first nontrivial Heegaard-Floer group 4533 6.The second nontrivial Heegaard-Floer group 4536 References 4542 Let s 2 be the Spin c class which corresponds to .0;1; 8/.The chain complex b CF .M; s 2 / is bigger, in comparison with b CF .M; s 1 /, and is generated by the following 72 generators: 1 D fx 1;1;2 ; x 2;2;4 ; x 3;4;1 ; x 4;5;1 ; x 5
Source: Algebraic & Geometric Topology
Authors: Neda Bagherifard, Eaman Eftekhary
Institution: Institute for Research in Fundamental Sciences
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4405637065