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On Construction of Signature of Quadratic Forms on Infinite-Dimensional Abstract Spaces

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Published/Copyright: February 25, 2010
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Georgian Mathematical Journal
From the journal Volume 9 Issue 4

Abstract

The signature of the Poincaré duality of compact topological manifolds with local system of coefficients can be described as a natural invariant of nondegenerate symmetric quadratic forms defined on a category of infinite dimensional linear spaces.

The objects of this category are linear spaces of the form W = V ⊕ V * where V is abstarct linear space with countable base. The space W is considered with minimal natural topology.

The symmetric quadratic form on the space W is generated by the Poincaré duality homomorphism on the abstract cochain group induced by nerves of the system of atlases of charts on the topological manifold.

Key words and phrases:: Poincaré duality; signature; topological manifolds
Received: 2002-07-22
Published Online: 2010-02-25
Published in Print: 2002-December

© Heldermann Verlag

Articles in the same Issue

  1. A Duality on Simplicial Complexes
  2. Chain Theories and Simplicial Abelian Group Spectra
  3. Crossed Complexes, and Free Crossed Resolutions for Amalgamated Sums and HNN-Extensions of Groups
  4. Boolean Galois Theories
  5. Stem Extensions and Stem Covers of Leibniz Algebras
  6. Central Series for Groups with Action and Leibniz Algebras
  7. Roots of Unity as A Lie Algebra
  8. On the Equivalence of Quillen's and Swan's K-Theories
  9. A Magnus–Witt Type Isomorphism for Non-Free Groups
  10. The Whitehead Categorical Group of Derivations
  11. Differential Equations, Spencer Cohomology, and Computing Resolutions
  12. On Construction of Signature of Quadratic Forms on Infinite-Dimensional Abstract Spaces
  13. A Property of the Degree Filtration of Polynomial Functors
  14. Free Quillen Factorization Systems
https://doi.org/10.1515/GMJ.2002.775
Keywords for this article
Poincaré duality; signature; topological manifolds

Articles in the same Issue

  1. A Duality on Simplicial Complexes
  2. Chain Theories and Simplicial Abelian Group Spectra
  3. Crossed Complexes, and Free Crossed Resolutions for Amalgamated Sums and HNN-Extensions of Groups
  4. Boolean Galois Theories
  5. Stem Extensions and Stem Covers of Leibniz Algebras
  6. Central Series for Groups with Action and Leibniz Algebras
  7. Roots of Unity as A Lie Algebra
  8. On the Equivalence of Quillen's and Swan's K-Theories
  9. A Magnus–Witt Type Isomorphism for Non-Free Groups
  10. The Whitehead Categorical Group of Derivations
  11. Differential Equations, Spencer Cohomology, and Computing Resolutions
  12. On Construction of Signature of Quadratic Forms on Infinite-Dimensional Abstract Spaces
  13. A Property of the Degree Filtration of Polynomial Functors
  14. Free Quillen Factorization Systems
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