System Upgrade on Tue, May 28th, 2024 at 2am (EDT)
Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.
This lecture notes is based on a sequence of lectures on Reidemeister torsions by V Turaev.
J Milnor showed that Reidemeister torsions and the Alexander polynomials are deeply related. By the surgery formulas of Reidemeister torsions, we can apply them to Dehn surgery problems, namely to lens and Seifert surgery problems, and to amphicheirality problem of a link. Since Reidemeister torsions of rational homology 3-spheres are elements in cyclotomic fields, we need algebraic number theoretical studies.
Recently P Ozsvath and Z Szabo defined the Heegaard Floer homology which is a powerful invariant to study 3-manifolds. It induces the Reidemeister-Turaev torsion. We also explain it here.
Contents:
- Preface
- Reidemeister Torsions
- Dehn Surgery
- Amphicheirality
- Algebraic Number Theory
- Heegaard Floer Homology
- Appendices:
- Chinese Remainder Theorem
- Proof of Franz Lemma
- Reidemeister-Schreier Method
Readership: Graduate students and researchers in topology.
