## $$w$$-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

### Keywords:

homology cobordism; Donaldson theory; Seiberg-Witten theory
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### References:

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