Invariants for families of Brieskorn varieties

Lawson, Terry

doi:10.1090/S0002-9939-1987-0866451-X

Invariants for families of Brieskorn varieties
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Proc. Amer. Math. Soc. 99 (1987), 187-192 Request permission

Abstract:

Fintushel and Stern have defined invariants for certain homology $3$-spheres which, if positive, show that the homology $3$-sphere cannot bound a positive definite $4$-manifold with no $2$-torsion in its first homology. In this note a number-theoretic formula is given for these invariants. It is used to show that all members of certain families of Brieskorn varieties have the same invariants, and hence exhibit the same nonbounding when one of the invariants is positive.

References

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Ronald Fintushel and Ronald J. Stern, Pseudofree orbifolds, Ann. of Math. (2) 122 (1985), no. 2, 335–364. MR 808222, DOI 10.2307/1971306

actions on the

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Terry Lawson, Representing homology classes of almost definite $4$-manifolds, Michigan Math. J. 34 (1987), no. 1, 85–91. MR 873022, DOI 10.1307/mmj/1029003485
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