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A geometrical procedure for killing the middle dimensional homology groups of algebraic hypersurfaces


Author: A. S. Libgober
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
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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 Levine's 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 [Enhancements On Off] (What's this?)

  • [1] S. Morita, The Kervaire invariant of hypersurfaces in complex projective spaces, Comment. Math. Helv. 50 (1975), 403-419. MR 52 #6756. MR 0385897 (52:6756)
  • [2] J. Wood, Removing handles from nonsingular algebraic hypersurfaces in $ C{P_{n + 1}}$, Invent. Math. 31 (1975), 1-3. MR 0388417 (52:9253)
  • [3] J. Levine, Polynomial invariant of knots of codimension two, Ann. of Math. (2) 84 (1966), 537-554. MR 0200922 (34:808)
  • [4] C. T. C. Wall, Classification of $ (n - 1)$-connected 2n-manifolds, Ann. of Math. (2) 75 (1962), 163-198. MR 26 #3071. MR 0145540 (26:3071)
  • [5] J. Milnor and P. Orlik, Isolated singularity defined by weighted homogeneous polynomials, Topology 9 (1970), 385-393. MR 45 #2757. MR 0293680 (45:2757)

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DOI: https://doi.org/10.1090/S0002-9939-1977-0440576-9
Article copyright: © Copyright 1977 American Mathematical Society

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