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For questions about Heegaard-Floer homology (as introduced by Ozsváth-Szabó in 2003) and its uses in 3- and 4-dimensional topology.

24 votes
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Can infinitely many alternating knots have the same Alexander polynomial?

No, there cannot exist infinitely many alternating knots with the same Alexander polynomial. To see why, suppose for the contrary that $K$ belongs to an infinite family $\{K_n\}_{n\in\mathbb{Z}}$ of …
Allison H. Moore's user avatar
20 votes

Introductory article of knot Heegaard Floer Homology

(Since this is just a string of references, I do not believe this constitutes a 'real answer' but it is too long for a comment, so I'm placing it in the answer field. Editors, please feel free to corr …
Allison H. Moore's user avatar