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Abstract We consider manifold-knot pairs$$(Y,K)$$, whereYis a homology 3-sphere that bounds a homology 4-ball. We show that the minimum genus of a PL surface$$\Sigma $$in a homology ballX, such that$$\partial (X, \Sigma ) = (Y, K)$$can be arbitrarily large. Equivalently, the minimum genus of a surface cobordism in a homology cobordism from$$(Y, K)$$to any knot in$$S^3$$can be arbitrarily large. The proof relies on Heegaard Floer homology.
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A note on PL-disks and rationally slice knots
We give infinitely many examples of manifold-knot pairs (Y, J) such that Y bounds an integer homology ball, J does not bound a non-locally-flat PL-disk in any integer homology ball, but J does bound a smoothly embedded disk in a rational homology ball. The proof relies on formal properties of involutive Heegaard Floer homology.
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- Award ID(s):
- 2019396
- PAR ID:
- 10613261
- Publisher / Repository:
- American Mathematical Society
- Date Published:
- Journal Name:
- Proceedings of symposia in pure mathematics
- ISSN:
- 0082-0717
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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