# An adjunction inequality for the Bauer-Furuta type invariants, with applications to sliceness and 4-manifold topology

@inproceedings{Iida2021AnAI, title={An adjunction inequality for the Bauer-Furuta type invariants, with applications to sliceness and 4-manifold topology}, author={Nobuo Iida and Anubhav Mukherjee and Masaki Taniguchi}, year={2021} }

We give infinitely many knots in S3 that are not smoothly H-slice (that is, bounding a null-homologous disk) in many 4-manifolds but they are topologically H-slice. In particular, we give such knots in punctured elliptic surfaces E(2n). In addition, we give obstructions to codimension-0 embedding of weak symplectic fillings with b3 = 0 into closed symplectic 4-manifolds with b1 = 0 and b + 2 ≡ 3 mod 4. We also show that any weakly symplectically fillable 3-manifold bounds a 4-manifold with at… Expand

#### 2 Citations

From zero surgeries to candidates for exotic definite four-manifolds

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One strategy for distinguishing smooth structures on closed 4-manifolds is to produce a knot K in S that is slice in one smooth filling W of S but not slice in some homeomorphic smooth filling W ′.… Expand

Involutions, knots, and Floer K-theory

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- 2021

We establish a version of Seiberg–Witten FloerK-theory for knots, as well as a version of Seiberg–Witten Floer K-theory for 3-manifolds with involutions. The main theorem is a 10/8-type inequality… Expand

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