✦ LIBER ✦
Casson invariant of cyclic coverings via eta-invariant and Dedekind sums
✍ Scribed by András Némethi
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 129 KB
- Volume
- 102
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
✦ Synopsis
Let Σ be a 3-dimensional oriented manifold and let K ⊂ Σ be a knot. We assume that Σ is an integer homology sphere and (Σ, K) has a plumbing representation. We denote the cyclic n-fold covering of Σ branched along K by Σ(K, n), and we assume that this manifold is integer homology sphere as well. If λ denotes the Casson invariant, then we show that λ(Σ(K, n))n • λ(Σ) can be computed from homological information only. More precisely, we compute in terms of an eta-typeinvariant associated with the isometric structure of the knot.