Invariants for families of Brieskorn varieties

Author:
Terry Lawson

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

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

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]**Ronald Fintushel and Terry Lawson,*Compactness of moduli spaces for orbifold instantons*, Topology Appl.**23**(1986), no. 3, 305–312. MR**858339**, 10.1016/0166-8641(85)90048-3**[FS1]**Ronald Fintushel and Ronald J. Stern,*Pseudofree orbifolds*, Ann. of Math. (2)**122**(1985), no. 2, 335–364. MR**808222**, 10.2307/1971306**[FS2]**-,*actions on the**-sphere*, Invent. Math. (to appear).**[L]**Terry Lawson,*Representing homology classes of almost definite 4-manifolds*, Michigan Math. J.**34**(1987), no. 1, 85–91. MR**873022**, 10.1307/mmj/1029003485**[N]**Walter D. Neumann,*An invariant of plumbed homology spheres*, Topology Symposium, Siegen 1979 (Proc. Sympos., Univ. Siegen, Siegen, 1979), Lecture Notes in Math., vol. 788, Springer, Berlin, 1980, pp. 125–144. MR**585657****[NZ]**Walter D. Neumann and Don Zagier,*A note on an invariant of Fintushel and Stern*, Geometry and topology (College Park, Md., 1983/84) Lecture Notes in Math., vol. 1167, Springer, Berlin, 1985, pp. 241–244. MR**827273**, 10.1007/BFb0075227

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

Article copyright:
© Copyright 1987
American Mathematical Society