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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Inner product spaces associated with Poincaré complexes


Authors: Seiya Sasao and Hideo Takahashi
Journal: Trans. Amer. Math. Soc. 260 (1980), 411-419
MSC: Primary 57P10
MathSciNet review: 574788
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Abstract: We consider the homotopy type classification of a certain kind of Poincaré complex. First we define an inner product space associated with such a Poincaré complex and we investigate the relation between the inner product space and the homotopy type of the Poincaré complex. As an application, some results for manifolds are proved.


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  • [1] William Browder, Surgery on simply-connected manifolds, Springer-Verlag, New York-Heidelberg, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 65. MR 0358813
  • [2] John Milnor and Dale Husemoller, Symmetric bilinear forms, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 73. MR 0506372
  • [3] C. T. C. Wall, Periodicity in algebraic 𝐿-theory, Manifolds—Tokyo 1973 (Proc. Internat. Conf., Tokyo, 1973) Univ. Tokyo Press, Tokyo, 1975, pp. 57–68. MR 0367021
  • [4] Seiya Sasao and Hideo Takahashi, Highly connected Poincaré complexes, Kodai Math. J. 2 (1979), no. 2, 139–147. MR 548390

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DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0574788-5
Article copyright: © Copyright 1980 American Mathematical Society