Contact cosmetic surgery on Legendrian knots in integer homology sphere $L$-spaces

Apratim Chakraborty; Swarup Kumar Das; Tanushree Shah

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arXiv · 2606.27485

Contact cosmetic surgery on Legendrian knots in integer homology sphere $L$-spaces

Apratim Chakraborty·Swarup Kumar Das·Tanushree Shah

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Abstract

We extend the study of contact cosmetic surgeries to Legendrian knots in integer homology sphere L-spaces . We prove that the contact cosmetic surgery conjecture holds for all non-trivial Legendrian knots in this setting, with the possible exception of Lagrangian slice knots. Our argument adapts and refines techniques from the S3 case to the broader context of L-spaces, incorporating constraints arising from Heegaard Floer theory

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Apratim Chakraborty, Swarup Kumar Das, Tanushree Shah. 2026-06-25. Contact cosmetic surgery on Legendrian knots in integer homology sphere $L$-spaces. https://arxiv.org/abs/2606.27485

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