Abstract
We prove that the (τ-weighted, sheaf-theoretic) SL(2, C) Casson–Lin invariant introduced by Manolescu and the first author is generically independent of the parameter τ and additive under connected sums of knots in integral homology 3-spheres. This addresses two questions asked by Manolescu and the first author. Our arguments involve a mix of topology and algebraic geometry, and rely crucially on the fact that the SL(2, C) Casson–Lin invariant admits an alternative interpretation via the theory of Behrend functions.
| Original language | English |
|---|---|
| Journal | Journal of the Mathematical Society of Japan |
| Volume | 74 |
| Issue number | 3 |
| Pages (from-to) | 683-717 |
| ISSN | 0025-5645 |
| DOIs | |
| Publication status | Published - Jul 2022 |
Funding
2020 Mathematics Subject Classification. Primary 57K10; Secondary 32S60, 57K18. Key Words and Phrases. sheaf-theoretic Floer homology, Casson–Lin invariants. The first author was supported by a Stanford University Benchmark Graduate Fellowship.
Keywords
- sheaf-theoretic Floer homology, Casson–Lin invariants
Fingerprint
Dive into the research topics of 'On the sheaf-theoretic SL(2, C) Casson–Lin invariant'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver