algebra. Both graded manifolds and supermanifolds are phrased in terms of sheaves of graded commutative algebras. However, graded manifolds are characterized...

the r-order jet manifold JrY of Y. A Lagrangian L can be introduced as an element of the variational bicomplex of the differential graded algebra O∗∞(Y)...

SUSY-manifold. SUSY-structure in dimension (1, k) is the same as odd contact structure. Superspace Supersymmetry Supergeometry Graded manifold Batalin–Vilkovisky...

differential graded category or DG category is a category whose morphism sets form differential graded Z {\displaystyle \mathbb {Z} } -modules. Graded manifold –...

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow...

Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds. Supergeometry is part and parcel of many classical...

related field of supergeometry where they enter into the definitions of graded manifolds, supermanifolds and superschemes. Let K be a commutative ring. In most...

R)=\bigoplus _{i}H^{i}(X,R)} into a graded ring, called the cohomology ring of X {\displaystyle X} . It is graded-commutative in the sense that: u v =...

Manifold injection is a mixture formation system for internal combustion engines with external mixture formation. It is commonly used in engines with spark...

differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. A differential graded algebra...

compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold. Two manifolds of the same...

the interior product acting on differential forms. Graded derivations of superalgebras (i.e. Z2-graded algebras) are often called superderivations. Hasse–Schmidt...

commutative graded ring, mimicking a theorem of Serre on Proj. Namely the category of quasicoherent sheaves of O-modules on a Proj of a commutative graded algebra...

geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear...

study of quantum groups. Manifolds with a Poisson algebra structure are known as Poisson manifolds, of which the symplectic manifolds and the Poisson–Lie groups...

are isomorphic (as graded rings), where the analogous product on singular cohomology is the cup product. For any smooth manifold M, let R _ {\textstyle...

bicomplex is a cochain complex of the differential graded algebra of exterior forms on jet manifolds of sections of a fiber bundle. Lagrangians and Euler–Lagrange...

naturally to the setting of graded commutative algebra, allowing for a natural foundation of calculus on supermanifolds, graded manifolds and associated concepts...

define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan...

extended to modules over a graded commutative algebra. This is the case of superconnections in supergeometry of graded manifolds and supervector bundles...

Conjecture (Thomas–Yau–Joyce): An oriented, graded, almost-calibrated Lagrangian L {\displaystyle L} splits as a graded Lagrangian connected sum L = L 1 # ⋯...

There are different descriptions of odd classical fields both on graded manifolds and supermanifolds. As above with classical fields, it is possible...

an algebraic variety V (which is nonsingular), or of a complex manifold, is the graded ring R ( V , K ) = R ( V , K V ) {\displaystyle R(V,K)=R(V,K_{V})\...

boundary, is a tamely graded Fréchet space, with any of the above graded structures. If M {\displaystyle M} is a compact smooth manifold and V → M {\displaystyle...

In mathematics, an alternating algebra is a Z-graded algebra for which xy = (−1)deg(x)deg(y)yx for all nonzero homogeneous elements x and y (i.e. it is...

Cavern and Thyrsis's Cave) is a natural cavern located at SK09865496 in the Manifold Valley of the White Peak in Staffordshire, England. It is classified as...

compact complex tori, K3 surfaces are the Calabi–Yau manifolds (and also the hyperkähler manifolds) of dimension two. As such, they are at the center of...

(4): 413–455. doi:10.24033/asens.1254. Kostant, Bertram (1977). "Graded manifolds, graded Lie theory, and prequantization". In: Differential Geometrical...

Hodge theory gives to the cohomology groups of a smooth and compact Kähler manifold. Hodge structures have been generalized for all complex varieties (even...

construction that produces a graded algebra out of a filtered algebra. If A {\displaystyle A} is a filtered algebra, then the associated graded algebra G ( A ) {\displaystyle...