The link surgery formula and equivariant surgeries

Kristen Hendricks; Abhishek Mallick; Matthew Stoffregen; Ian Zemke

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arXiv · 2507.12809

The link surgery formula and equivariant surgeries

Kristen Hendricks·Abhishek Mallick·Matthew Stoffregen·Ian Zemke

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Abstract

We prove an equivariant version of the Heegaard Floer link surgery formula. As a special case, this gives an equivariant knot surgery formula for equivariant knots in $S^3$. Our proof goes by way of a naturality theorem for certain bordered modules described by the last author. As a sample application, we prove the kernel of the forgetful map from the equivariant homology cobordism group to the homology cobordism group contains a $\Z^\infty$-summand.

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Kristen Hendricks, Abhishek Mallick, Matthew Stoffregen, Ian Zemke. 2025-07-17. The link surgery formula and equivariant surgeries. https://arxiv.org/abs/2507.12809

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