منابع مشابه
Floer Homology and Invariants of Homology Cobordism
By using surgery techniques, we compute Floer homology for certain classes of integral homology 3-spheres homology cobordant to zero. We prove that Floer homology is two-periodic for all these manifolds. Based on this fact, we introduce a new integer valued invariant of integral homology 3-spheres. Our computations suggest its homology cobordism invariance.
متن کاملOn the Homology Cobordism Group of Homology 3-spheres
In this paper we present our results on the homology cobordism group Θ3Z of the oriented integral homology 3-spheres. We specially emphasize the role played in the subject by the gauge theory including Floer homology and invariants by Donaldson and Seiberg – Witten. A closed oriented 3-manifold Σ is said to be an integral homology sphere if it has the same integral homology as the 3-sphere S. T...
متن کاملHomology Cobordism and Classical Knot Invariants
In this paper we define and investigate Z2–homology cobordism invariants of Z2–homology 3–spheres which turn out to be related to classical invariants of knots. As an application we show that many lens spaces have infinite order in the Z2–homology cobordism group and we prove a lower bound for the slice genus of a knot on which integral surgery yields a given Z2– homology sphere. We also give s...
متن کاملKnot Concordance and Homology Cobordism Workshop
I will give an overview of the n-solvable filtration of the smooth knot (or string link) concordance group including the strategy and tools used to analyze it: higher-order Alexander modules, linking forms and signature defects. I will attempt to discuss what is known about this filtration, what is not known but should be knowable by present techniques; and discuss the failings of present techn...
متن کاملThe Cobordism Group of Homology Cylinders
Garoufalidis and Levine introduced the homology cobordism group of homology cylinders over a surface. This group can be regarded as a generalization of the mapping class group. Using torsion invariants, we show that the abelianization of this group is infinitely generated provided that the first Betti number of the surface is positive. In particular, this shows that the group is not perfect. Th...
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ژورنال
عنوان ژورنال: Topology
سال: 1971
ISSN: 0040-9383
DOI: 10.1016/0040-9383(71)90032-2