For every k, a 3-manifold with an involution has ordinary Dehn surgery number k and equivariant Dehn surgery number 2k.
The link surgery formula and equivariant surgeries
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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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Unbounded Gaps Between Ordinary and Equivariant Dehn Surgery Numbers
For every k, a 3-manifold with an involution has ordinary Dehn surgery number k and equivariant Dehn surgery number 2k.