منابع مشابه
Local formulae for combinatorial Pontrjagin classes
By p(|K|) denote the characteristic class of a combinatorial manifold K given by the polynomial p in Pontrjagin classes of K. We prove that for any polynomial p there exists a function taking each combinatorial manifold K to a rational simplicial cycle z(K) such that: (1) the Poincaré dual of z(K) represents the cohomology class p(|K|); (2) a coefficient of each simplex ∆ in the cycle z(K) is d...
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A combinatorial formula for the Pontrjagin classes of a triangulated manifold is given. The main ingredients are oriented matroid theory and a modified formulation of Chern-Weil theory.
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This paper shows how Hodge’s theory of harmonic p-sets (a discrete version of his theory of harmonic forms) allows a new approach to be taken to the problem of providing a combinatorial definition of the Pontrjagin classes of a compact manifold. This approach is then related to the author’s definition of flag vectors for hypergraphs, and other objects constructed out of vertices and cells. It i...
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We prove several finiteness results for the class Ma,b,π,n of n-manifolds that have fundamental groups isomorphic to π and that can be given complete Riemannian metrics of sectional curvatures within [a, b] where a ≤ b < 0. In particular, if M is a closed negatively curved manifold of dimension at least three, then only finitely many manifolds in the class Ma,b,π1(M),n are total spaces of vecto...
متن کاملCharacteristic Classes for Pl Micro Bundles
1. The method to prove Theorem I is to compute the Serre spectral sequences associated to the fiberings, SPL—>SF—>F/PL—>BSPL —>BSF. The structures of H*(SF:ZP) and H*(BSF:ZP) were determined in [9], [l6] and [17]. The homotopy type of F / P L is the deep result of Sullivan [15]. The first step is to study the H space structure of F / P L and the inclusion map &:SF—->F/PL. The main tool in this ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1973
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1973-13121-0