Plumbed homology 3-spheres bounding acyclic 4-manifolds (Q5939018)
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scientific article; zbMATH DE number 1624999
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Plumbed homology 3-spheres bounding acyclic 4-manifolds |
scientific article; zbMATH DE number 1624999 |
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Plumbed homology 3-spheres bounding acyclic 4-manifolds (English)
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27 June 2002
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cobordism invariant
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homology 3-spheres
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homology cobordism group
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Recall that a homology cobordism invariant of plumbed homology 3-spheres is defined by using the Seiberg-Witten monopole equation on 4-dimensional \(V\)-manifolds. [\textit{Y. Fukumoto} and \textit{M. Furuta}, Math. Res. Lett. 7, No. 5-6, 757-766 (2000; Zbl 0971.57026)].NEWLINENEWLINENEWLINEIn this paper, the author gives an explicit formula of such an invariant by applying the Atiyah-Singer-Kawasaki-V-index theorem. Especially this formula may provide a sufficient condition for homology 3-spheres of plumbing type to have infinite order in the homology cobordism group.
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