# Combinatorial hodge theory and signature operator

@article{Teleman1980CombinatorialHT,
title={Combinatorial hodge theory and signature operator},
author={Nicolae Teleman},
journal={Inventiones mathematicae},
year={1980},
volume={61},
pages={227-249}
}
This paper represents an detailed version of our paper [12] presented at the Hawaii Conference on the Geometry of the Laplace Operator, March 1979. In this paper we present the solution to the following problem posed by Singer in [8], w 4, concerning elliptical operators on PL-maifolds: "If M is a PL-manifold, the L-polynomials are still well defined (Thom [13]) from which one can still define the rational Pontrjagin classes. The Hirzebruch signature theorem still holds. Is there an associated… Expand
18 Citations
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© Publications mathématiques de l’I.H.É.S., 1983, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand
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Let $M$ be a closed symplectic manifold of dimension $2n$ with non-ellipticity. We can define an almost Kahler structure on $M$ by using the given symplectic form. Using Darboux coordinate charts, weExpand
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Let $\Gamma$ be a finite group acting on a smooth, compact manifold $M$, let $P \in \psi^m(M; E_0, E_1)$ be a $\Gamma$-invariant, classical pseudodifferential operator acting between sections of twoExpand

#### References

SHOWING 1-10 OF 10 REFERENCES
Global analysis on PL-manifolds
The paper deals mainly with combinatorial structures; in some cases we need refinements of combinatorial structures. Riemannian metrics are defined on any combinatorial manifold M. The existence ofExpand
Harmonic Integrals on Strongly Pseudo-Convex Manifolds: II
In this paper we prove the basic existence and regularity theorems for the a-Neumann problem (see Theorems 6.6 and 6.14). The results presented here were outlined by the author in [8]. In Part I ofExpand
An introduction to complex analysis in several variables
I. Analytic Functions of One Complex Variable. II. Elementary Properties of Functions of Several Complex Variables. III. Applications to Commutative Banach Algebras. IV. L2 Estimates and ExistenceExpand
Singular Integrals and Di?erentiability Properties of Functions
A plurality of disks include solid laserable material and are in parallel spaced apart relation within a transparent tubular enclosure. Spaces between the disks constitute portions of a collant fluidExpand
Espaces intermédiaires entre espaces de Sobolev avec poids
© Scuola Normale Superiore, Pisa, 1963, tous droits réservés. L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze »Expand