Abstract
Every Brieskorn homology sphere Σ(p, q, r) is a double cover of the 3-sphere ramified over a Montesinos knot k(p, q, r). We express the Floer homology of Σ(p, q, r) in terms of certain invariants of the knot k(p, q, r), among which are the knot signature and the Jones polynomial. We also define an integer valued invariant of integral homology 3-spheres which agrees with the μ̄-invariant of W. Neumann and L. Siebenmann for Seifert fibered homology spheres, and investigate its behavior with respect to homology 4-cobordism.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 15-87 |
| Number of pages | 73 |
| Journal | Journal of Differential Geometry |
| Volume | 53 |
| Issue number | 1 |
| State | Published - Sep 1999 |
| Externally published | Yes |
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Keywords
- Casson invariant
- Floer homology
- Homology cobordism
- Jones polynomial
- Knot signature
- Montesinos knots
- Seifert manifolds
ASJC Scopus subject areas
- Algebra and Number Theory
- Analysis
- Geometry and Topology
Cite this
Floer homology of Brieskorn homology spheres. / Saveliev, Nikolai.
In: Journal of Differential Geometry, Vol. 53, No. 1, 09.1999, p. 15-87.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Floer homology of Brieskorn homology spheres
AU - Saveliev, Nikolai
PY - 1999/9
Y1 - 1999/9
N2 - Every Brieskorn homology sphere Σ(p, q, r) is a double cover of the 3-sphere ramified over a Montesinos knot k(p, q, r). We express the Floer homology of Σ(p, q, r) in terms of certain invariants of the knot k(p, q, r), among which are the knot signature and the Jones polynomial. We also define an integer valued invariant of integral homology 3-spheres which agrees with the μ̄-invariant of W. Neumann and L. Siebenmann for Seifert fibered homology spheres, and investigate its behavior with respect to homology 4-cobordism.
AB - Every Brieskorn homology sphere Σ(p, q, r) is a double cover of the 3-sphere ramified over a Montesinos knot k(p, q, r). We express the Floer homology of Σ(p, q, r) in terms of certain invariants of the knot k(p, q, r), among which are the knot signature and the Jones polynomial. We also define an integer valued invariant of integral homology 3-spheres which agrees with the μ̄-invariant of W. Neumann and L. Siebenmann for Seifert fibered homology spheres, and investigate its behavior with respect to homology 4-cobordism.
KW - Casson invariant
KW - Floer homology
KW - Homology cobordism
KW - Jones polynomial
KW - Knot signature
KW - Montesinos knots
KW - Seifert manifolds
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UR - http://www.scopus.com/inward/citedby.url?scp=0002521843&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0002521843
VL - 53
SP - 15
EP - 87
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
SN - 0022-040X
IS - 1
ER -