MathSciDoc: An Archive for Mathematician ∫

 
Log In
Sign Up
Help
Go
 

On the monopole Lefschetz number of finite order diffeomorphisms

林剑锋 清华大学丘成桐数学科学中心 Daniel Ruberman Brandeis University Nikolai Saveliev University of Miami

Geometric Analysis and Geometric Topology mathscidoc:2205.15005

Geometry & Topology, 25, 2021.7
Let K be a knot in an integral homology 3-sphere Y, and Σ the corresponding n-fold cyclic branched cover. Assuming that Σ is a rational homology sphere (which is always the case when n is a prime power), we give a formula for the Lefschetz number of the action that the covering translation induces on the reduced monopole homology of Σ. The proof relies on a careful analysis of the Seiberg--Witten equations on 3-orbifolds and of various η-invariants. We give several applications of our formula: (1) we calculate the Seiberg--Witten and Furuta--Ohta invariants for the mapping tori of all semi-free actions of Z/n on integral homology 3-spheres; (2) we give a novel obstruction (in terms of the Jones polynomial) for the branched cover of a knot in S3 being an L-space; (3) we give a new set of knot concordance invariants in terms of the monopole Lefschetz numbers of covering translations on the branched covers.
No keywords uploaded!
[ Download ] [ 2022-05-17 17:44:30 uploaded by linjian5477 ] [ 553 downloads ] [ 0 comments ] 
@inproceedings{林剑锋2021on,
  title={On the monopole Lefschetz number of finite order diffeomorphisms},
  author={林剑锋, Daniel Ruberman, and Nikolai Saveliev},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517174430807766250},
  booktitle={Geometry & Topology},
  volume={25},
  year={2021},
}
林剑锋, Daniel Ruberman, and Nikolai Saveliev. On the monopole Lefschetz number of finite order diffeomorphisms. 2021. Vol. 25. In Geometry & Topology. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517174430807766250.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved