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Abstract A previous result about the decategorified bordered (sutured) Heegaard Floer invariants of surfaces glued together along intervals, generalizing the decategorified content of Rouquier and the author’s higher-tensor-product-based gluing theorem in cornered Heegaard Floer homology, was proved only over $${\mathbb{F}}_2$$ and without gradings. In this paper we add signs and prove a graded version of the interval gluing theorem over $${\mathbb{Z}}$$, enabling a more detailed comparison of these aspects of decategorified Heegaard Floer theory with modern work on non-semisimple 3d TQFTs in mathematics and physics.
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This content will become publicly available on September 18, 2026
Diagonals and A-Infinity Tensor Products
Extending work of Saneblidze–Umble and others, we use diagonals for the associahedron and multiplihedron to define tensor products of𝐴∞-algebras, modules, algebra homomorphisms, and module morphisms, as well as to define a bimodule analogue of twisted complexes (typeDDstructures, in the language of bordered Heegaard Floer homology) and their one- and two-sided tensor products. We then give analogous definitions for 1-parameter deformations of𝐴∞-algebras; this involves another collection of complexes. These constructions are relevant to bordered Heegaard Floer homology.
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- PAR ID:
- 10636694
- Publisher / Repository:
- Akadémiai Kiadó
- Date Published:
- Journal Name:
- Studia Scientiarum Mathematicarum Hungarica
- Volume:
- 62
- Issue:
- 2-3
- ISSN:
- 0081-6906
- Page Range / eLocation ID:
- 97 to 304
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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