Invariants for families of Brieskorn varieties

Author:
Terry Lawson

Journal:
Proc. Amer. Math. Soc. **99** (1987), 187-192

MSC:
Primary 57R90; Secondary 57N13, 57R55

DOI:
https://doi.org/10.1090/S0002-9939-1987-0866451-X

MathSciNet review:
866451

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Abstract: Fintushel and Stern have defined invariants for certain homology -spheres which, if positive, show that the homology -sphere cannot bound a positive definite -manifold with no -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.

**[FL]**R. Fintushel and T. Lawson,*Compactness of moduli spaces for orbifold instantons*, Topology Appl. (to appear). MR**858339 (88e:57017)****[FS1]**R. Fintushel and R. Stern,*Pseudofree orbifolds*, Ann. of Math. (2)**122**(1985), 335-364. MR**808222 (87a:57027)****[FS2]**-,*actions on the**-sphere*, Invent. Math. (to appear).**[L]**T. Lawson,*Representing homology classes on almost definite**-manifolds*, Michigan Math. J. (to appear). MR**873022 (88d:57024)****[N]**W. Neumann,*An invariant of plumbed homology spheres*, Topology Symposium, Siegen, 1979, Lecture Notes in Math., vol. 788, Springer-Verlag, Berlin and New York, 1979, pp. 125-144. MR**585657 (82j:57033)****[NZ]**W. Neumann and D. Zagier,*A Note on an invariant of Fintushel and Stern*, Geometry and Topology (Proceedings, Univ. of Maryland, 1983-84), Lecture Notes in Math., vol. 1167, Springer-Verlag, Berlin and New York, 1985, pp. 241-244. MR**827273 (87e:57020)**

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0866451-X

Article copyright:
© Copyright 1987
American Mathematical Society