# “Nonlinear pullbacks” of functions and L∞-morphisms for homotopy Poisson structures

@article{Voronov2017NonlinearPO, title={“Nonlinear pullbacks” of functions and L∞-morphisms for homotopy Poisson structures}, author={Theodore Th. Voronov}, journal={Journal of Geometry and Physics}, year={2017}, volume={111}, pages={94-110} }

## 13 Citations

Microformal Geometry and Homotopy Algebras

- MathematicsProceedings of the Steklov Institute of Mathematics
- 2018

We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal, or “thick,” morphisms. They are formal canonical relations of a special form, constructed…

Tangent functor on microformal morphisms

- Mathematics
- 2017

We show how the tangent functor extends naturally from ordinary smooth maps to "microformal" (or "thick") morphisms of supermanifolds, a notion that we introduced earlier. Microformal morphisms…

L-infinity bialgebroids and homotopy Poisson structures on supermanifolds

- Mathematics
- 2019

We generalize to the homotopy case a result of K. Mackenzie and P. Xu on relation between Lie bialgebroids and Poisson geometry. For a homotopy Poisson structure on a supermanifold $M$, we show that…

Graded Geometry, Q‐Manifolds, and Microformal Geometry

- MathematicsFortschritte der Physik
- 2019

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. They can be seen as a…

Non-linear homomorphisms of algebras of functions are induced by thick morphisms.

- Mathematics
- 2020

In 2014, Voronov introduced the notion of thick morphisms of (super)manifolds as a tool for constructing $L_{\infty}$-morphisms of homotopy Poisson algebras. Thick morphisms generalise ordinary…

Thick morphisms, higher Koszul brackets, and $L_{\infty}$-algebroids

- Mathematics
- 2018

It is a classical fact in Poisson geometry that the cotangent bundle of a Poisson manifold has the structure of a Lie algebroid. Manifestations of this structure are the Lichnerowicz differential on…

On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms

- Mathematics
- 2020

Thick morphisms of supermanifolds, quantum mechanics, and spinor representation

- MathematicsJournal of Geometry and Physics
- 2020

Symplectic microgeometry, IV: Quantization

- MathematicsPacific Journal of Mathematics
- 2021

We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the…

Shifted Derived Poisson Manifolds Associated with Lie Pairs

- MathematicsCommunications in Mathematical Physics
- 2019

We study the shifted analogue of the “Lie–Poisson” construction for $$L_\infty $$ L ∞ algebroids and we prove that any $$L_\infty $$ L ∞ algebroid naturally gives rise to shifted derived Poisson…

## References

SHOWING 1-10 OF 29 REFERENCES

Thick morphisms of supermanifolds and oscillatory integral operators

- Mathematics
- 2016

We show that thick morphisms (or microformal morphisms) between smooth (super)manifolds, introduced by us before, are classical limits of 'quantum thick morphisms' defined here as particular…

Deformation Quantization of Poisson Manifolds

- Mathematics
- 1997

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the…

Quantum microformal morphisms of supermanifolds: an explicit formula and further properties

- Mathematics
- 2015

We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially…

Noncommutative Differential Forms and Quantization of the Odd Symplectic Category

- Mathematics
- 2002

There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for all functions f and g. We notice that this noncommutative…

Symplectic Categories

- Mathematics
- 2009

Quantization problems suggest that the category of symplectic manifolds and symplectomorphisms be augmented by the inclusion of canonical relations as morphisms. These relations compose well when a…

Graded Manifolds and Drinfeld Doubles for Lie Bialgebroids

- Mathematics
- 2001

We define graded manifolds as a version of supermanifolds endowed with an extra Z-grading in the structure sheaf, called weight (not linked
with parity). Examples are ordinary supermanifolds, vector…

On Odd Laplace Operators

- Mathematics
- 2002

We consider odd Laplace operators acting on densities of various weights on an odd Poisson (= Schouten) manifold M. We prove that the case of densities of weight 1/2 (half-densities) is distinguished…

EXTENSION OF REPRESENTATIONS OF THE CLASSICAL GROUPS TO REPRESENT A nONS OF CA TEGORIES

- Mathematics
- 2005

It is shown that with each series An, Bn, Cn, Dn ofthe complex classical Lie groups a certain category GA, B, C, D is connected in a natural fashion. A finitedimensional representation of any…

Introduction to SH Lie algebras for physicists

- Mathematics
- 1993

UNC-MATH-92/2originally April 27, 1990, revised September 24, 1992INTRODUCTION TO SH LIE ALGEBRAS FOR PHYSICISTSTom LadaJim StasheffMuch of point particle physics can be described in terms of Lie…