Degree-1 maps and rank inequalities in Heegaard Floer homology

Fraser Binns; Sudipta Ghosh

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arXiv · 2504.19871

Degree-1 maps and rank inequalities in Heegaard Floer homology

Fraser Binns·Sudipta Ghosh

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Abstract

Ghosh-Sivek-Zentner constructed degree-1 maps from certain rational homology solid tori to the twisted $I$-bundle over the Klein bottle. We show that these maps yield rank inequalities for Heegaard Floer homology. To do so, we use Hanselman-Rasmussen-Watson's immersed curve interpretation of bordered Floer homology, extending their proof of a similar rank inequality corresponding to degree-1 maps to the solid torus. Our result provides further evidence for Kronheimer-Mowka's conjectured relationship between Heegaard Floer homology and instanton Floer homology.

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Fraser Binns, Sudipta Ghosh. 2025-04-28. Degree-1 maps and rank inequalities in Heegaard Floer homology. https://arxiv.org/abs/2504.19871

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