Topic
Euler characteristic
About: Euler characteristic is a research topic. Over the lifetime, 2803 publications have been published within this topic receiving 44546 citations. The topic is also known as: Euler-Poincaré characteristic.
Papers published on a yearly basis
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Papers
7 May 1998
TL;DR: In this article, the authors give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis, and cover the monotonicity theorem, cell decomposition, and the Euler characteristic in the ominimal setting and show how these notions are easier to handle than in ordinary topology.
Abstract: Following their introduction in the early 1980s o-minimal structures were found to provide an elegant and surprisingly efficient generalization of semialgebraic and subanalytic geometry. These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. The book starts with an introduction and overview of the subject. Later chapters cover the monotonicity theorem, cell decomposition, and the Euler characteristic in the o-minimal setting and show how these notions are easier to handle than in ordinary topology. The remarkable combinatorial property of o-minimal structures, the Vapnik-Chervonenkis property, is also covered. This book should be of interest to model theorists, analytic geometers and topologists.
1,442 citations
TL;DR: In this article, it was shown that the Teichmiiller space can be interpreted as the orbifold Euler characteristic of the moduli space of curves of genus g with base point.
Abstract: Let Fg 1, g> 1, be the mapping class group consisting of all isotopy classes of base-point and orientation preserving homeomorphisms of a closed, oriented surface F of genus g. Let )~(~1) be its Euler characteristic in the sense of Wall, that is Z(F~I)= [Fgl: F] l z(E/F), where F is any torsion free subgroup of finite index in F~ 1 and E is a contractible space on which F acts freely and properly discontinuously. An example of such a space is the Teichmiiller space ~-~1, and g(F~ ~) can be interpreted as the orbifold Euler characteristic of ~-~'/F~I =JOin, the moduli space of curves of genus g with base point. The purpose of this paper is to prove the following formula for )~(F~I):
866 citations
TL;DR: Khovanov et al. as mentioned in this paper constructed a doubly-graded homology theory of links with the Euler characteristic, which is based on matrix factorizations, which provide a linear algebra description of maximal Cohen-Macaulay modules on isolated hypersurface singularities.
Abstract: Author(s): Khovanov, Mikhail; Rozansky, Lev | Abstract: For each positive integer n the HOMFLY polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a doubly-graded homology theory of links with this polynomial as the Euler characteristic. The core of our construction utilizes the theory of matrix factorizations, which provide a linear algebra description of maximal Cohen-Macaulay modules on isolated hypersurface singularities.
813 citations
TL;DR: The unbiased and model-free method is used on a series of 3-D reconstructions of canceous bone specimens, and it is demonstrated that the connectivity of cancellous bone is not simply related to volume fraction (density), and that biased andmodel-based 2-D methods aimed at determining connectivity do not have any general relationship to connectivity in cancellousBone.
727 citations
TL;DR: In this article, a universal system of differential equations is proposed to determine the generating function of the Chern classes of the Hodge bundle in Gromov-Witten theory for any target X. The genus g, degree d multiple cover contribution of a rational curve is found to be simply proportional to the Euler characteristic of M_g.
Abstract: Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these integrals from the standard descendent potential (for any target X). We use virtual localization and classical degeneracy calculations to find trigonometric closed form solutions for special Hodge integrals over the moduli space of pointed curves. These formulas are applied to two computations in Gromov-Witten theory for Calabi-Yau 3-folds. The genus g, degree d multiple cover contribution of a rational curve is found to be simply proportional to the Euler characteristic of M_g. The genus g, degree 0 Gromov-Witten invariant is calculated (in agreement with recent string theoretic calculations of Gopakumar-Vafa and Marino-Moore). Finally, with Zagier's help, our Hodge integral formulas imply a general genus prediction of the punctual Virasoro constraints applied to the projective line.
707 citations
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| Year | Papers |
|---|---|
| 2025 | 13 |
| 2024 | 23 |
| 2023 | 83 |
| 2022 | 126 |
| 2021 | 128 |
| 2020 | 147 |