w-Invariants and the Fintushel–Stern Invariants for Plumbed Homology 3-Spheres

Abstract

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.

2000 AMS Subject Classification:

• Primary 57R90
• Secondary 55-04

Keywords:

• Homology cobordism
• Donaldson theory
• Seiberg-Witten theory

ACKNOWLEDGMENTS

I am grateful to Mikio Furuta and Masaaki Ue for all their valuable comments and encouragement. The research for this paper was supported by MEXT Grant-in-Aid for Scientific Research (18740039).