An equality on Hochschild homology groups

1997 ◽  
Vol 42 (8) ◽  
pp. 624-627 ◽  
Author(s):  
Pu Zhang ◽  
Shaoxue Liu
Keyword(s):  
Hochschild Homology ◽  
Homology Groups

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 TRIPLY-GRADED LINK HOMOLOGY AND HOCHSCHILD HOMOLOGY OF SOERGEL BIMODULES

2007 ◽  
Vol 18 (08) ◽  
pp. 869-885 ◽  
Author(s):  
MIKHAIL KHOVANOV
Keyword(s):  
Group Action ◽  
Braid Group ◽  
Polynomial Algebra ◽  
Homology Theory ◽  
Hochschild Homology ◽  
Polynomial Algebras ◽  
Homology Groups ◽  
Link Homology ◽  
Soergel Bimodules ◽  
Braid Group Action

We consider a class of bimodules over polynomial algebras which were originally introduced by Soergel in relation to the Kazhdan–Lusztig theory, and which describe a direct summand of the category of Harish–Chandra modules for sl(n). Rouquier used Soergel bimodules to construct a braid group action on the homotopy category of complexes of modules over a polynomial algebra. We apply Hochschild homology to Rouquier's complexes and produce triply-graded homology groups associated to a braid. These groups turn out to be isomorphic to the groups previously defined by Lev Rozansky and the author, which depend, up to isomorphism and overall shift, only on the closure of the braid. Consequently, our construction produces a homology theory for links.

scholarly journals Hochschild Homology Groups of System Quiver Algebras of Minimal Wild Type

2012 ◽  
Vol 25 ◽  
pp. 2081-2088
Author(s):  
Zhibing Liu ◽  
Huixia Wang ◽  
Guiju Liu ◽  
Fang He
Keyword(s):  
Hochschild Homology ◽  
Wild Type ◽  
Homology Groups

scholarly journals Homology and residues of adiabatic pseudodifferential operators

2004 ◽  
Vol 175 ◽  
pp. 171-221 ◽  
Author(s):  
Sergiu Moroianu
Keyword(s):  
Existence And Uniqueness ◽  
Pseudodifferential Operators ◽  
Hochschild Homology ◽  
Total Space ◽  
Homology Groups ◽  
Noncommutative Residue

AbstractWe compute the Hochschild homology groups of the adiabatic algebra Ψa(X), a deformation of the algebra of pseudodifferential operators Ψ(X) when X is the total space of a fibration of closed manifolds. We deduce the existence and uniqueness of traces on Ψa(X) and some of its ideals and quotients, in the spirit of the noncommutative residue of Wodzicki and Guillemin. We introduce certain higher homological versions of the residue trace. When the base of the fibration is S1, these functionals are related to the η function of Atiyah-Patodi-Singer.

scholarly journals Hochschild Homology Groups of System Quiver Algebras of Maximal Tame Type

2017 ◽  
Vol 7 (4) ◽  
pp. 259-267
Author(s):  
Chunling He ◽  
◽  
Huiru Chen ◽  
Zhibing Liu
Keyword(s):  
Hochschild Homology ◽  
Homology Groups

scholarly journals Profinite rigidity for twisted Alexander polynomials

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jun Ueki
Keyword(s):  
Rigidity Theorem ◽  
Homology Groups ◽  
Alexander Polynomials ◽  
Twisted Homology ◽  
Hyperbolic Volumes

AbstractWe formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the twisted homology groups in a {{\mathbb{Z}}}-cover of a 3-manifold with use of Mahler measures. We examine several examples associated to Riley’s parabolic representations of two-bridge knot groups and give a remark on hyperbolic volumes.

scholarly journals Path homology theory of edge-colored graphs

2021 ◽  
Vol 19 (1) ◽  
pp. 706-723
Author(s):  
Yuri V. Muranov ◽  
Anna Szczepkowska
Keyword(s):  
Spectral Sequence ◽  
Edge Coloring ◽  
Homology Theory ◽  
Homotopy Category ◽  
Homology Groups ◽  
Colored Graphs ◽  
Natural Filtration ◽  
Definition Of ◽  
Exact Sequences

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.

Exponents for extraordinary homology groups

1993 ◽  
Vol 68 (1) ◽  
pp. 653-672 ◽  
Author(s):  
Dominique Arlettaz
Keyword(s):  
Homology Groups
Sign in / Sign up

Export Citation Format

Share Document