A geometrical procedure for killing the middle dimensional homology groups of algebraic hypersurfaces
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- by A. S. Libgober PDF
- Proc. Amer. Math. Soc. 63 (1977), 198-202 Request permission
Abstract:
Explicit construction for decomposition of algebraic hypersurfaces into a connected sum of handles and a homological projective space is discussed. Also a connection is provided between Levineβs results about the Arf invariant in the theory of knots and the computation of Arf invariant of hypersurfaces by S. Morita and J. Wood.References
- Shigeyuki Morita, The Kervaire invariant of hypersurfaces in complex projective spaces, Comment. Math. Helv. 50 (1975), no.Β 3, 403β419. MR 385897, DOI 10.1007/BF02565759
- John W. Wood, Removing handles from non-singular algebraic hypersurfaces in $CP_{n+1}$, Invent. Math. 31 (1975), no.Β 1, 1β6. MR 388417, DOI 10.1007/BF01389862
- J. Levine, Polynomial invariants of knots of codimension two, Ann. of Math. (2) 84 (1966), 537β554. MR 200922, DOI 10.2307/1970459
- C. T. C. Wall, Classification of $(n-1)$-connected $2n$-manifolds, Ann. of Math. (2) 75 (1962), 163β189. MR 145540, DOI 10.2307/1970425
- John Milnor and Peter Orlik, Isolated singularities defined by weighted homogeneous polynomials, Topology 9 (1970), 385β393. MR 293680, DOI 10.1016/0040-9383(70)90061-3
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 198-202
- MSC: Primary 57D65; Secondary 14B05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0440576-9
- MathSciNet review: 0440576