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Canadian journal of mathematics, ISSN 0008-414X, 10/2019, Volume 71, Issue 5, pp. 1209 - 1241
...}$ a coherent sheaf on a smooth projective manifold $X$ over an algebraic closed field of characteristic $0... 
Article | MATHEMATICS | deformation of manifold and coherent sheaf | differential graded Lie algebra | OBSTRUCTIONS | Mathematics - Algebraic Geometry
Journal Article
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS, ISSN 0015-8208, 08/2019, Volume 67, Issue 8-9, p. 1910023
Journal Article
International Journal of Mechanical Sciences, ISSN 0020-7403, 11/2018, Volume 148, pp. 103 - 117
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2016, Volume 283, Issue 2, pp. 449 - 482
Geometric structures on NQ-manifolds, i.e., nonnegatively graded manifolds with a homological vector field, encode nongraded geometric data on Lie algebroids and their higher analogues... 
Lie algebroids | Graded manifolds | Spencer operators | NQ-manifolds | Vector bundle valued differential forms | MATHEMATICS | graded manifolds | JACOBI STRUCTURES | vector bundle valued differential forms | GEOMETRY
Journal Article
Advances in Mathematics, ISSN 0001-8708, 01/2017, Volume 304, pp. 1156 - 1175
We prove unobstructed deformations for compact Kählerian even-dimensional Poisson manifolds whose Poisson tensor degenerates along a divisor with mild singularities... 
Symplectic structure | Deformation theory | Log complex | Complex structure | Poisson structure | Differential graded Lie algebra | Mixed Hodge theory | Schouten algebra
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 06/2018, pp. 1 - 51
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 2012, Volume 62, Issue 2, pp. 464 - 478
In this paper we study the problem of small deformations of D-structures on compact manifolds... 
Para-complex structure | Deformation | Para-CR structure | Differential graded Lie algebra | CR D-structure | D-structure | MATHEMATICS | PHYSICS, MATHEMATICAL
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 2/2019, Volume 109, Issue 2, pp. 243 - 293
...}$$ Z -graded manifolds of degree $$\le 2$$ ≤ 2 . Indeed, a link has been established between the super and classical pictures by the geometrization process, leading to an equivalence of the category of $$\mathbb {Z... 
Geometry | Double vector bundle | 32C11 | Theoretical, Mathematical and Computational Physics | Complex Systems | Lie algebroid | Graded manifold | Group Theory and Generalizations | 51P05 | Physics | 53D17
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 04/2014, Volume 16, Issue 2, pp. 1350015 - 1-1350015-37
We study intrinsic deformations of Levi flat structures on a smooth manifold. A Levi flat structure on a smooth manifold L is a couple (ξ, J) where ξ ⊂ T(L... 
Nijenhuis tensor | Levi flat structures | Maurer-Cartan equation | differential graded Lie algebras | complex Lie algebras of derivation type | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | FOLIATION | 3-MANIFOLDS | Manifolds | Deltas | Deformation | Mathematical analysis | Flats | Lie groups | Texts | Joining | Mathematics - Complex Variables
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 2009, Volume 59, Issue 9, pp. 1285 - 1305
A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F... 
Lie bialgebroids | Courant algebroids | Drinfeld doubles | BRST formalism | Double vector bundles | Graded super-manifolds | LEGENDRE TRANSFORMATION | 2ND-ORDER GEOMETRY | TANGENT | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DUALITY | LIFTS | Mathematics - Differential Geometry
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 02/2018, Volume 68, Issue 1, pp. 181 - 196
Let G(n, k) denote the complex Grassmann manifold of k-dimensional vector subspaces of C-n. Assume l,k <= [/2... 
Grassmann manifold | homotopy class of maps | cohomology algebra | graded algebra homomorphism | MATHEMATICS | COHOMOLOGY | SELF-MAPS | AUTOMORPHISMS | Manifolds (Mathematics) | Homotopy theory | Research | Mathematical research | Mappings (Mathematics) | Subspaces | Maps
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 07/2013, Volume 10, Issue 6
Generalized current algebras introduced by Alekseev and Strobl in two dimensions are reconstructed by a graded manifold and a graded Poisson brackets... 
QP-manifolds | Dirac structure | differential graded manifolds | Current algebras | DIRAC STRUCTURES | PHYSICS, MATHEMATICAL | GEOMETRY
Journal Article
Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 02/2018, Volume 19, Issue 2, pp. 1 - 35
We study the germs at the origin of G -representation varieties and the degree 1 cohomology jump loci of fundamental groups of quasi-projective manifolds. Using the Morgan... 
admissible map | representation variety | differential graded algebra model | quasi-projective manifold | holonomy Lie algebra | semisimple Lie algebra | cohomology jump loci | analytic germ | Deligne weight filtration | variety of flat connections | REPRESENTATIONS | VARIETIES | MATHEMATICS | COHOMOLOGY | GEOMETRY | Homology | Inclusions | Loci | Subgroups | Linear algebra
Journal Article
Homology, Homotopy and Applications, ISSN 1532-0073, 2012, Volume 14, Issue 2, pp. 63 - 75
.... Geometric examples include the shifted de Rham complex of a Poisson manifold and the subcomplex of differential forms on a symplectic manifold vanishing on a Lagrangian submanifold, endowed with the Koszul bracket... 
Batalin-Vilkovisky algebra | Homotopical algebra | Differential graded Lie algebra | Deformation theory | Poisson manifold | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | homotopical algebra | differential graded Lie algebra | deformation theory | 13D10 | 18G55 | 53D17
Journal Article
Proceedings of the Japan Academy Series A: Mathematical Sciences, ISSN 0386-2194, 01/2013, Volume 89, Issue 1, pp. 15 - 19
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 7/2013, Volume 103, Issue 7, pp. 729 - 741
Journal Article
Engineering Analysis with Boundary Elements, ISSN 0955-7997, 03/2018, Volume 88, pp. 145 - 155
Journal Article
Fortschritte der Physik, ISSN 0015-8208, 08/2019, Volume 67, Issue 8-9, p. n/a
We give an exposition of graded and microformal geometry, and the language of Q‐manifolds. Q‐manifolds are supermanifolds endowed with an odd vector field of square zero... 
thick morphism | homotopy bracket | graded manifold | microformal morphism
Journal Article
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