scholarly journals Poisson homology in degree 0 for some rings of symplectic invariants

2009 ◽  
Vol 322 (10) ◽  
pp. 3580-3613 ◽  
Author(s):  
Frédéric Butin
Keyword(s):  
Poisson Homology ◽  
Symplectic Invariants

scholarly journals Residues and homology for pseudodifferential operators on foliations

2004 ◽  
Vol 94 (1) ◽  
pp. 75 ◽  
Author(s):  
M.-T. Benameur ◽  
V. Nistor
Keyword(s):  
Diophantine Approximation ◽  
Pseudodifferential Operators ◽  
Hochschild Homology ◽  
Foliated Manifold ◽  
Homology Groups ◽  
General Properties ◽  
Poisson Homology ◽  
Foliated Manifolds

We study the Hochschild homology groups of the algebra of complete symbols on a foliated manifold $(M,F)$. The first step is to relate these groups to the Poisson homology of $(M,F)$ and of other related foliated manifolds. We then establish several general properties of the Poisson homology groups of foliated manifolds. As an example, we completely determine these Hochschild homology groups for the algebra of complete symbols on the irrational slope foliation of a torus (under some diophantine approximation assumptions). We also use our calculations to determine all residue traces on algebras of pseudodifferential operators along the leaves of a foliation.

scholarly journals A note on the duality between Poisson homology and cohomology

2020 ◽  
Vol 48 (10) ◽  
pp. 4170-4175
Author(s):  
Jiafeng Lü ◽  
Xingting Wang ◽  
Guangbin Zhuang
Keyword(s):  
Poisson Homology

scholarly journals Poisson brackets and symplectic invariants

2011 ◽  
Vol 18 (1) ◽  
pp. 89-157 ◽  
Author(s):  
Lev Buhovsky ◽  
Michael Entov ◽  
Leonid Polterovich
Keyword(s):  
Poisson Brackets ◽  
Symplectic Invariants

scholarly journals On (co)homology of Frobenius Poisson algebras

2014 ◽  
Vol 14 (2) ◽  
pp. 371-386 ◽  
Author(s):  
Can Zhu ◽  
Fred Van Oystaeyen ◽  
Yinhuo Zhang
Keyword(s):  
Bilinear Form ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Poisson Algebra ◽  
Hochschild Homology ◽  
Poisson Algebras ◽  
Poisson Homology ◽  
Poisson Cohomology ◽  
Frobenius Algebras

AbstractIn this paper, we study Poisson (co)homology of a Frobenius Poisson algebra. More precisely, we show that there exists a duality between Poisson homology and Poisson cohomology of Frobenius Poisson algebras, similar to that between Hochschild homology and Hochschild cohomology of Frobenius algebras. Then we use the non-degenerate bilinear form on a unimodular Frobenius Poisson algebra to construct a Batalin-Vilkovisky structure on the Poisson cohomology ring making it into a Batalin-Vilkovisky algebra.

scholarly journals Fundamental groups of complements of plane curves and symplectic invariants

Topology ◽  
2004 ◽  
Vol 43 (6) ◽  
pp. 1285-1318 ◽  
Author(s):  
D. Auroux ◽  
S.K. Donaldson ◽  
L. Katzarkov ◽  
M. Yotov
Keyword(s):  
Plane Curves ◽  
Fundamental Groups ◽  
Symplectic Invariants

scholarly journals Symplectic T7, T8 singularities and Lagrangian tangency orders

2012 ◽  
Vol 55 (3) ◽  
pp. 657-683 ◽  
Author(s):  
Wojciech Domitrz ◽  
Żaneta Trȩbska
Keyword(s):  
Geometric Description ◽  
Symplectic Invariants

AbstractWe study the local symplectic algebra of curves. We use the method of algebraic restrictions to classify symplectic T7, T8 singularities. We define discrete symplectic invariants (the Lagrangian tangency orders) and compare them with the index of isotropy. We use these invariants to distinguish symplectic singularities of classical T7 singularity. We also give the geometric description of symplectic classes of the singularity.

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