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Relevant bibliographies by topics / Graded manifold

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Journal articles

Academic literature on the topic 'Graded manifold'

Author: Grafiati

Published: 10 March 2023

Last updated: 11 March 2023

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Journal articles on the topic "Graded manifold"

1

Sardanashvily, G., and W. Wachowski. "Differential Calculus onN-Graded Manifolds." Journal of Mathematics 2017 (2017): 1–19. http://dx.doi.org/10.1155/2017/8271562.

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The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, overN-graded commutative rings and onN-graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and onZ2-graded manifolds. We follow the notion of anN-graded manifold as a local-ringed space whose body is a smooth manifoldZ. A key point is that the graded derivation module of the structure ring of graded functions

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2

Ševera, Pavol, and Michal Širaň. "Integration of Differential Graded Manifolds." International Mathematics Research Notices 2020, no. 20 (2019): 6769–814. http://dx.doi.org/10.1093/imrn/rnz004.

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Abstract We consider the problem of integration of $L_\infty $-algebroids (differential non-negatively graded manifolds) to $L_\infty $-groupoids. We first construct a “big” Kan simplicial manifold (Fréchet or Banach) whose points are solutions of a (generalized) Maurer–Cartan equation. The main analytic trick in our work is an integral transformation sending the solutions of the Maurer–Cartan equation to closed differential forms. Following the ideas of Ezra Getzler, we then impose a gauge condition that cuts out a finite-dimensional simplicial submanifold. This “smaller” simplicial manifold

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3

Bruce, Andrew James, and Janusz Grabowski. "Riemannian Structures on Z 2 n -Manifolds." Mathematics 8, no. 9 (2020): 1469. http://dx.doi.org/10.3390/math8091469.

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Very loosely, Z2n-manifolds are ‘manifolds’ with Z2n-graded coordinates and their sign rule is determined by the scalar product of their Z2n-degrees. A little more carefully, such objects can be understood within a sheaf-theoretical framework, just as supermanifolds can, but with subtle differences. In this paper, we examine the notion of a Riemannian Z2n-manifold, i.e., a Z2n-manifold equipped with a Riemannian metric that may carry non-zero Z2n-degree. We show that the basic notions and tenets of Riemannian geometry directly generalize to the setting of Z2n-geometry. For example, the Fundame

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4

De Nicola, Antonio, and Ivan Yudin. "Generalized Goldberg Formula." Canadian Mathematical Bulletin 59, no. 3 (2016): 508–20. http://dx.doi.org/10.4153/cmb-2016-007-4.

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AbstractIn this paper we prove a useful formula for the graded commutator of the Hodge codifferential with the left wedge multiplication by a fixed p-form acting on the de Rham algebra of a Riemannian manifold. Our formula generalizes a formula stated by Samuel I. Goldberg for the case of 1-forms. As first examples of application we obtain new identities on locally conformally Kähler manifolds and quasi-Sasakian manifolds. Moreover, we prove that under suitable conditions a certain subalgebra of differential forms in a compact manifold is quasi-isomorphic as a CDGA to the full de Rham algebra.

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5

Kotov, Alexei, and Thomas Strobl. "Characteristic classes associated to Q-bundles." International Journal of Geometric Methods in Modern Physics 12, no. 01 (2014): 1550006. http://dx.doi.org/10.1142/s0219887815500061.

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A Q-manifold is a graded manifold endowed with a vector field of degree 1 squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of "gauge fields" (sections in the category of graded manifolds) and each cohomology class of a certain subcomplex of forms on the fiber we associate a cohomology class on the base. As any principal bundle yields canonically a Q-bundle, this construction generalizes Chern–Weil classes. Novel examples include cohomology classes that are locally de Rham differential of the integrands of top

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6

Tahora, Saraban, and Khondokar M. Ahmed. "Study on De Rham Cohomology Algebra of Manifolds." Dhaka University Journal of Science 64, no. 2 (2016): 109–13. http://dx.doi.org/10.3329/dujs.v64i2.54484.

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In the present paper some aspects of exterior derivative, graded algebra, cohomology algebra, de Rham cohomology algebra, singular homology, cohomology class are studied. Graded subspace, smooth map, a singular P- - simplex in a manifold M, oriented n- manifold M, the space of P- cycles and P- boundaries, Pth singular homology and homology class are treated in our paper. A theorem 3.03 is established which is related to orientable manifold. Dhaka Univ. J. Sci. 64(2): 109-113, 2016 (July)

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7

GILLE, CATHERINE. "ON THE LE-MURAKAMI-OHTSUKI INVARIANT IN DEGREE 2 FOR SEVERAL CLASSES OF 3-MANIFOLDS." Journal of Knot Theory and Its Ramifications 12, no. 01 (2003): 17–45. http://dx.doi.org/10.1142/s0218216503002287.

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The 3-manifolds invariant of Le, Murakami and Ohtsuki is the universal finite type invariant for integral homology spheres. It takes values in the graded algebra of trivalent graphs and it is known that its degree one part is essentially the Casson-Walker-Lescop invariant. Here we compute the degree two term for several classes of 3-manifolds. In particular, we give an expression of ω (ML) up to order 2 when MLis the 3-manifold obtained by Dehn surgery along a framed link L with one or two components.

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8

IKEDA, NORIAKI, and KOZO KOIZUMI. "CURRENT ALGEBRAS AND QP-MANIFOLDS." International Journal of Geometric Methods in Modern Physics 10, no. 06 (2013): 1350024. http://dx.doi.org/10.1142/s0219887813500242.

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Generalized current algebras introduced by Alekseev and Strobl in two dimensions are reconstructed by a graded manifold and a graded Poisson brackets. We generalize their current algebras to higher dimensions. QP-manifolds provide the unified structures of current algebras in any dimension. Current algebras give rise to structures of Leibniz/Loday algebroids, which are characterized by QP-structures. Especially, in three dimensions, a current algebra has a structure of a Lie algebroid up to homotopy introduced by Uchino and one of the authors, which has a bracket of a generalization of the Cou

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9

Paepe, Karl De. "Graded subalgebras of the Lie algebra of a smooth manifold." International Journal of Mathematics and Mathematical Sciences 27, no. 3 (2001): 141–48. http://dx.doi.org/10.1155/s0161171201010511.

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10

Gualtieri, Marco, Mykola Matviichuk, and Geoffrey Scott. "Deformation of Dirac Structures via L∞ Algebras." International Mathematics Research Notices 2020, no. 14 (2018): 4295–323. http://dx.doi.org/10.1093/imrn/rny134.

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Abstract The deformation theory of a Dirac structure is controlled by a differential graded Lie algebra that depends on the choice of an auxiliary transversal Dirac structure; if the transversal is not involutive, one obtains an $L_\infty $ algebra instead. We develop a simplified method for describing this $L_\infty $ algebra and use it to prove that the $L_\infty $ algebras corresponding to different transversals are canonically $L_\infty $–isomorphic. In some cases, this isomorphism provides a formality map, as we show in several examples including (quasi)-Poisson geometry, Dirac structures

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