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\(w\)-invariants and the Fintushel-Stern invariants for plumbed homology 3-spheres. (English) Zbl 1262.57016

Summary: In this paper, we present numerical computations of the \(w\)-invariants and the Fintushel-Stern invariants for plumbed homology 3-spheres and use the results to test a conjecture of Witten suggesting that the invariants carry equivalent information. While the two invariants give nearly the same information for some homology 3-spheres, we present numerous examples in which the information carried by the two invariants is quite different.

MSC:

57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57R90 Other types of cobordism
57-04 Software, source code, etc. for problems pertaining to manifolds and cell complexes
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References:

[1] Casson [Casson and Harer 81] A., Pacific J. Math. 96 pp 23– (1981)
[2] Fintushel [Fintushel and Lawson 86] R., Topology Appl. 23 pp 305– (1986) · Zbl 0664.57006
[3] Fintushel [Fintushel and Stern 85] R., Ann. Math. 122 pp 335– (1985) · Zbl 0602.57013
[4] Froyshov [Froyshov 96] K., Math. Res. Lett. 3 pp 373– (1996) · Zbl 0872.57024
[5] Fukumoto [Fukumoto 00] Y., J. Math. Kyoto Univ. 40 pp 729– (2000)
[6] Fukumoto [Fukumoto and Furuta 00] Y., Math. Res. Lett. 7 pp 757– (2000) · Zbl 0971.57026
[7] Fukumoto [Fukumoto et al. 01] Y., Topology and Its Appl. 116 pp 333– (2001) · Zbl 0991.57019
[8] Furuta [Furuta 01] M., Math. Res. Lett. 8 pp 279– (2001) · Zbl 0984.57011
[9] Kawasaki [Kawasaki 81] T., Nagoya Math. J. 84 pp 135– (1981) · Zbl 0437.58020
[10] Lawson [Lawson 88] T., Math. Z. 200 pp 123– (1988) · Zbl 0641.57006
[11] Neumann [Neumann 81] W., Trans. Amer. Math. Soc. 268 pp 299– (1981)
[12] Saveliev [Saveliev 02] N., Pacific J. Math 205 pp 465– (2002) · Zbl 1053.57012
[13] Satake [Satake 57] I., J. of the Math. Soc. of Japan 9 pp 464– (1957) · Zbl 0080.37403
[14] Uhlenbeck [Uhlenbeck 82a] K., Commun. Math. Phys. 83 pp 31– (1982) · Zbl 0499.58019
[15] Uhlenbeck [Uhlenbeck 82b] K., Commun. Math. Phys. 83 pp 11– (1982) · Zbl 0491.58032
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