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Reviews in Mathematical Physics, ISSN 0129-055X, 10/2016, Volume 28, Issue 9, p. 1650021
We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in... 
supersymmetry | matrix models | N Q-manifolds | multisymplectic geometry | higher gauge theory | Analysis | Algebra
Journal Article
Journal of geometry and physics, ISSN 0393-0440, 2019, Volume 142, pp. 254 - 273
Pre-Courant algebroids are ‘Courant algebroids’ without the Jacobi identity for the Courant–Dorfman bracket. We examine the corresponding supermanifold... 
Q-manifolds | Supermanifolds | Courant algebroids | VB-Courant algebroids | Cochain complex | TANGENT LIFTS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DIRAC STRUCTURES | GRADED BUNDLES | MANIFOLDS | GEOMETRY
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 03/2016, Volume 101, pp. 71 - 99
Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as... 
Poisson structures | Vector bundles | Lie algebroids | Lie groupoids | Graded manifolds | MATHEMATICS | MECHANICS | Q-MANIFOLDS | PHYSICS, MATHEMATICAL
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 12/2014, Volume 86, pp. 497 - 533
We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six space–time... 
Superconformal models | [formula omitted]-manifolds | Tensor hierarchy | [formula omitted]-infinity algebras | Q-manifolds | L-infinity algebras | MATHEMATICS | GAUGE ALGEBRA | POISSON SIGMA-MODELS | PHYSICS, MATHEMATICAL | Analysis | Algebra
Journal Article
Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, 8/2018, Volume 302, Issue 1, pp. 88 - 129
We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal, or “thick,” morphisms. They are formal canonical... 
Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | Q-MANIFOLDS | MORPHISMS
Journal Article
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 11/2016, Volume 12
We construct the full linearisation functor which takes a graded bundle of degree k (a particular kind of graded manifold) and produces a k-fold vector bundle.... 
Polarisation | Supermanifolds | N-manifolds | Graded manifolds | K-fold vector bundles | supermani-folds | k-fold vector bundles | HIGHER-ORDER | POISSON | polarisation | LIE ALGEBROIDS | graded manifolds | Q-MANIFOLDS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL
Journal Article
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, ISSN 1815-0659, 2018, Volume 14
We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of... 
CLASSICAL PSEUDOGROUPS | QUANTUM | PHYSICS, MATHEMATICAL | almost-Lie algebroid | variational principle | graded bundle | LAGRANGIAN SUBMANIFOLDS | MECHANICS | graded manifold | higher algebroid | vector bundle comorphism | GRADED BUNDLES | DYNAMICS | Q-MANIFOLDS | DUALITY | VARIATIONAL-PROBLEMS | algebroid lift | Bundling | Axioms
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 12/2015, Volume 105, Issue 12, pp. 1735 - 1783
A construction of gauge-invariant observables is suggested for a class of topological field theories, the AKSZ sigma models. The observables are associated to... 
Geometry | Q-manifolds | observables | Batalin–Vilkovisky formalism | 57R56 | Theoretical, Mathematical and Computational Physics | 81T70 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | 58A50 | Topological field theory | Physics
Journal Article
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, ISSN 0219-8878, 01/2015, Volume 12, Issue 1, pp. 1550006 - 1-1550006-26
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... 
Q-manifolds | gauge theories | characteristic classes | PHYSICS, MATHEMATICAL | Manifolds | Bundling | Construction | Categories | Lie groups | Fields (mathematics) | Topology | Gages | Fibers
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 12/2010, Volume 94, Issue 3, pp. 243 - 261
An odd vector field Q on a supermanifold M is called homological, if Q 2 = 0. The operator of Lie derivative L Q makes the algebra of smooth tensor fields on M... 
Geometry | Q -manifolds | gauge theories | Theoretical, Mathematical and Computational Physics | 81T70 | Group Theory and Generalizations | 57R32 | characteristic classes | Statistical Physics, Dynamical Systems and Complexity | 58A50 | Physics | Q-manifolds | LIE | PHYSICS, MATHEMATICAL | ALGEBRA
Journal Article
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 11/2015, Volume 11
We define and make initial study of Lie groupoids equipped with a compatible homogeneity (or graded bundle) structure, such objects we will refer to as... 
Homogeneity structures | Lie algebroids | Lie groupoids | Graded manifolds | homogeneity structures | BRACKETS | ALGEBROIDS | INTEGRABILITY | graded manifolds | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | JACOBI | INTEGRATION | Q-MANIFOLDS | FORMALISM | CONTACT GROUPOIDS
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 01/2015, Volume 87, pp. 422 - 431
We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant... 
[formula omitted]-manifolds | Twisted Poisson sigma model | Courant algebroids | Equivariant cohomology | Gauging | Q-manifolds | MATHEMATICS | PHYSICS, MATHEMATICAL | Mathematical Physics | Mathematics
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 8/2012, Volume 140, Issue 8, pp. 2855 - 2872
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 12/2019, Volume 67, p. 101556
Quotients of Banach-Lie groups are regarded as topological groups with Lie algebra in the sense of Hofmann-Morris on the one hand, and as Q-groups in the sense... 
Topological group with Lie algebra | Q-manifold | Banach-Lie group | MATHEMATICS | MATHEMATICS, APPLIED | VECTORS
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 2010, Volume 60, Issue 5, pp. 729 - 759
A Q -manifold M is a supermanifold endowed with an odd vector field Q squaring to zero. The Lie derivative L Q along Q makes the algebra of smooth tensor... 
[formula omitted]-manifolds | Gauge theories | Characteristic classes | Q-manifolds | MATHEMATICS, APPLIED | COHOMOLOGY | MASTER EQUATION | LIE ALGEBROIDS | POISSON MANIFOLD | MODULAR CLASS | QUANTIZATION | PHYSICS, MATHEMATICAL | GEOMETRY
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 10/2009, Volume 242, Issue 2, pp. 311 - 332
We approach Mackenzie's LA-groupoids from a supergeometric point of view by introducing Q-groupoids, which are groupoid objects in the category of Q-manifolds.... 
Q-manifolds | Lie algebroids | Lie groupoids | Simplicial manifolds | Equivariant cohomology | MATHEMATICS | simplicial manifolds | DOUBLE LIE ALGEBROIDS | SPACES | 2ND-ORDER GEOMETRY | MAP | equivariant cohomology
Journal Article
Archivum Mathematicum, ISSN 0044-8753, 2017, Volume 53, Issue 4, pp. 203 - 219
Archivum Mathematicum, vol. 53 (2017), issue 4, pp. 203-219 A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion... 
Modular classes | Higher Poisson manifolds | Q-manifolds | Characteristic classes | algebroids
Journal Article
Dissertationes Mathematicae, ISSN 0012-3862, 2013, Issue 491, pp. 1 - 120
General position properties play a crucial role in geometric and infinite-dimensional topologies. Often such properties provide convenient tools for... 
Embedding | Z | set | Disjoint n-cells property | point | DENDRITES | disjoint n-cells property | Z-point | APPROXIMATION | FUNCTION SPACES | EXTENSION | Z(n)-set | DIVISION | ANRS | MATHEMATICS | DIMENSIONAL MAPS | SELECTION THEOREM | Q-MANIFOLDS | MAPPINGS | embedding
Journal Article
Mathematical Notes, ISSN 0001-4346, 12/1997, Volume 62, Issue 6, pp. 683 - 687
The hyperspace of all convex bodies of constant width in Euclidean spaceR n ,n≥2, is proved to be homeomorphic to a contractibleQ-manifold (Q denotes the... 
Q -manifolds | constant width bodies | retraction | Mathematics, general | Mathematics | hyperspace of convex bodies | infinite-dimensional topology | Q-manifolds | Infinite-dimensional topology | Retraction | Constant width bodies | Hyperspace of convex bodies | MATHEMATICS
Journal Article
Topology and its Applications, ISSN 0166-8641, 1993, Volume 53, Issue 1, pp. 7 - 18
Let X be a nondiscrete metric compactum and Y an Euclidean polyhedron without isolated points or a Lipschitz n-manifold ( n > 0). Let LIP( X, Y) w be the space... 
The weak topology | Lipschitz manifold | ANLE | Euclidean polyhedron | The space of Lipschitz maps | Q∞-manifold | The direct limit | manifold
Journal Article
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