Quotient $$(\Gamma ,R)$$ ( Γ , R ) -hypermodules and homology algebra

2015 ◽  
Vol 27 (3-4) ◽  
pp. 353-364
Author(s):  
S. Ostadhadi-Dehkordi
Keyword(s):  
Homology Algebra

scholarly journals On the quantum homology algebra of toric Fano manifolds

2009 ◽  
Vol 15 (1) ◽  
pp. 121-149 ◽  
Author(s):  
Yaron Ostrover ◽  
Ilya Tyomkin
Keyword(s):  
Fano Manifolds ◽  
Quantum Homology ◽  
Homology Algebra

scholarly journals Inverse System in The Category of Intuitionistic Fuzzy Soft Modules

2018 ◽  
Vol 14 (1) ◽  
pp. 7486-7502
Author(s):  
S. E. Abdullayev ◽  
Sadi Bayramov
Keyword(s):  
Exact Sequence ◽  
Inverse Limit ◽  
Inverse System ◽  
Derived Functor ◽  
Intuitionistic Fuzzy ◽  
Homology Algebra ◽  
Basic Concepts ◽  
Exact Sequences

This paper begins with the basic concepts of soft module. Later, we introduce inverse system in the category of intutionistic fuzzy soft modules and prove that its limit exists in this category. Generally, limit of inverse system of exact sequences of intutionistic fuzzy soft modules is not exact. Then we define the notion  which is first derived functor of the inverse limit functor. Finally, using methods of homology algebra, we prove that the inverse system limit of exact sequence of intutionistic fuzzy soft modules is exact.

scholarly journals The Milnor-Moore theorem for $$L_\infty $$ algebras in rational homotopy theory

2021 ◽  
Author(s):  
José Manuel Moreno Fernández
Keyword(s):  
Homotopy Theory ◽  
Homotopy Groups ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Massey Products ◽  
Homotopy Types ◽  
Homology Algebra ◽  
Simply Connected ◽  
Space Homology ◽  
Loop Space Homology

AbstractWe give a construction of the universal enveloping $$A_\infty $$ A ∞ algebra of a given $$L_\infty $$ L ∞ algebra, alternative to the already existing versions. As applications, we derive a higher homotopy algebras version of the classical Milnor-Moore theorem. This proposes a new $$A_\infty $$ A ∞ model for simply connected rational homotopy types, and uncovers a relationship between the higher order rational Whitehead products in homotopy groups and the Pontryagin-Massey products in the rational loop space homology algebra.

scholarly journals CONTACT HOMOLOGY OF LEFT-HANDED STABILIZATIONS AND PLUMBING OF OPEN BOOKS

2010 ◽  
Vol 12 (02) ◽  
pp. 223-263 ◽  
Author(s):  
FRÉDÉRIC BOURGEOIS ◽  
OTTO VAN KOERT
Keyword(s):  
Contact Manifold ◽  
Finite Energy ◽  
Unit Element ◽  
Contact Homology ◽  
Connected Sums ◽  
Open Books ◽  
Left Handed ◽  
Closed Contact ◽  
Homology Algebra ◽  
Energy Plane

We show that on any closed contact manifold of dimension greater than 1 a contact structure with vanishing contact homology can be constructed. The basic idea for the construction comes from Giroux. We use a special open book decomposition for spheres. The page is the cotangent bundle of a sphere and the monodromy is given by a left-handed Dehn twist. In the resulting contact manifold, we exhibit a closed Reeb orbit that bounds a single finite energy plane like in the computation for the overtwisted case. As a result, the unit element of the contact homology algebra is exact and so the contact homology vanishes. This result can be extended to other contact manifolds by using connected sums. The latter is related to the plumbing or 2-Murasugi sum of contact open books. We shall give a possible description of this construction and some conjectures about the plumbing operation.

scholarly journals Homological Invariants of Local Rings

1963 ◽  
Vol 22 ◽  
pp. 219-227 ◽  
Author(s):  
Hiroshi Uehara
Keyword(s):  
Local Ring ◽  
Betti Numbers ◽  
Residue Field ◽  
Unit Element ◽  
Minimal System ◽  
Local Rings ◽  
Homology Algebra ◽  
Homological Invariants ◽  
Minimal System Of Generators ◽  
The Relationship

In this paper R is a commutative noetherian local ring with unit element 1 and M is its maximal ideal. Let K be the residue field R/M and let {t1,t2,…, tn) be a minimal system of generators for M. By a complex R<T1. . ., Tp> we mean an R-algebra* obtained by the adjunction of the variables T1. . ., Tp of degree 1 which kill t1,…, tp. The main purpose of this paper is, among other things, to construct an R-algebra resolution of the field K, so that we can investigate the relationship between the homology algebra H (R < T1,…, Tn>) and the homological invariants of R such as the algebra TorR(K, K) and the Betti numbers Bp = dimk TorR(K, K) of the local ring R. The relationship was initially studied by Serre [5].

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