Introduction to supergeometry

Abstract

These notes are based on a series of lectures given by the first author at the school of `Poisson 2010', held at IMPA, Rio de Janeiro. They contain an exposition of the theory of super- and graded manifolds, cohomological vector fields, graded symplectic structures, reduction and the AKSZ-formalism.

Lecture notes of a course held at the school Poisson 2010 at IMPA, July 2010; 21 pages; references improved

References in corpus (1)

• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories

Cited by in corpus (38)

• Even symplectic supermanifolds and double field theory
• Representations of Homotopy Lie-Rinehart Algebras
• Linear duals of graded bundles and higher analogues of (Lie) algebroids
• Lie algebroid modules and representations up to homotopy
• Simultaneous deformations and Poisson geometry
• Introduction to graded geometry
• The Chern-Simons current in systems of DNA-RNA transcriptions
• Global Theory of Graded Manifolds
• Introduction to the BV-BFV formalism
• Differential graded contact geometry and Jacobi structures
• Anomaly on Superspace of Time Series Data
• Vector Bundle Valued Differential Forms on $\mathbb{N}Q$-manifolds
• Higher Lie algebra actions on Lie algebroids
• Courant cohomology, Cartan calculus, connections, curvature, characteristic classes
• Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket
• Dg manifolds, formal exponential maps and homotopy Lie algebras
• Algebraic formulation of higher gauge theory
• The geometry of graded cotangent bundles
• Deformed graded Poisson structures, Generalized Geometry and Supergravity
• Monoidally graded manifolds
• Graded Generalized Geometry
• Geometric BV for twisted Courant sigma models and the BRST power finesse
• Atiyah classes and Todd classes of pullback dg Lie algebroids associated with Lie pairs
• Higher algebraic structures in Hamiltonian Floer theory
• Keller admissible triples and Duflo theorem
• Ruelle zeta function from field theory
• Exact renormalization group in Batalin--Vilkovisky theory
• Quantum field theoretic representation of Wilson surfaces: I higher coadjoint orbit theory
• Threefold Nature of Graded Vector Bundles
• Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models
• Dimensional reduction of Courant sigma models and Lie theory of Poisson groupoids
• Poly-symplectic Geometry and the AKSZ Formalism
• $A_{\infty }$-Algebras from Lie Pairs
• Gravity from AKSZ-Manin theories in two, three, and four dimensions
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Stability of fixed points in Poisson geometry and higher Lie theory
• Instances of Higher Geometry in Field Theory
• Quantizing Derived Mapping Stacks