The formal Kuranishi parameterization via the universal homological perturbation theory solution of the deformation equation

2018 ◽  
Vol 25 (4) ◽  
pp. 529-544 ◽  
Author(s):  
Johannes Huebschmann
Keyword(s):  
Perturbation Theory ◽  
Deformation Problem ◽  
Deformation Equation ◽  
Homological Perturbation Theory ◽  
Graded Lie Algebra ◽  
Differential Graded Lie Algebra ◽  
Homological Perturbation ◽  
Theory Solution ◽  
Formal Version ◽  
Algebra Over A Field

AbstractUsing homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero. Our approach includes a formal version of the Kuranishi method in the theory of deformations of complex manifolds.

Cohomology of Homotopy 2-types

2019 ◽  
pp. 379-422
Author(s):  
Graham Ellis
Keyword(s):  
Perturbation Theory ◽  
Projective Plane ◽  
Integral Homology ◽  
Homotopy Classes ◽  
Cw Complex ◽  
Crossed Modules ◽  
Homological Perturbation Theory ◽  
Homological Perturbation ◽  
Manual Classification

This chapter introduces some of the basic ingredients in the classification of homotopy 2-types and describes datatypes and algorithms for implementing them on a computer. These are illustrated using computer examples involving: the fundamental crossed modules of a CW-complex, cat-1-groups, simplicial groups, Moore complexes, the Dold-Kan correspondence, integral homology of simplicial groups, homological perturbation theory. A manual classification of homotopy classes of maps from a surface to the projective plane is also included.

Cartan's constructions and the twisted Eilenberg–Zilber theorem

2010 ◽  
Vol 17 (1) ◽  
pp. 13-23
Author(s):  
Víctor Álvarez ◽  
José Andrés Armario ◽  
María Dolores Frau ◽  
Pedro Real
Keyword(s):  
Perturbation Theory ◽  
Tensor Product ◽  
Cartesian Product ◽  
Tensor Products ◽  
Standard Product ◽  
Homological Perturbation Theory ◽  
Twisted Tensor Product ◽  
Homological Perturbation ◽  
Twisted Cartesian Product

Abstract Let 𝐺 × τ 𝐺′ be the principal twisted Cartesian product with fibre 𝐺, base 𝐺 and twisting function where 𝐺 and 𝐺′ are simplicial groups as well as 𝐺 × τ 𝐺′; and 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁 (𝐺′) be the twisted tensor product associated to 𝐶𝑁 (𝐺 × τ 𝐺′) by the twisted Eilenberg–Zilber theorem. Here we prove that the pair 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁(𝐺′), μ) is a multiplicative Cartan's construction where μ is the standard product on 𝐶𝑁(𝐺) ⊗ 𝐶𝑁(𝐺′). Furthermore, assuming that a contraction from 𝐶𝑁(𝐺′) to 𝐻𝐺′ exists and using the techniques from homological perturbation theory, we extend the former result to other “twisted” tensor products of the form 𝐶𝑁(𝐺) ⊗ 𝐻𝐺′.

scholarly journals LAGRANGIAN Sp(3) BRST SYMMETRY FOR IRREDUCIBLE GAUGE THEORIES

2001 ◽  
Vol 16 (17) ◽  
pp. 2975-3009 ◽  
Author(s):  
C. BIZDADEA ◽  
S. O. SALIU
Keyword(s):  
Perturbation Theory ◽  
Effective Action ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Gauge Fixing ◽  
Homological Perturbation Theory ◽  
Canonical Generator ◽  
Homological Perturbation

The Lagrangian Sp(3) BRST symmetry for irreducible gauge theories is constructed in the framework of homological perturbation theory. The canonical generator of this extended symmetry is shown to exist. A gauge-fixing procedure specific to the standard antibracket–antifield formalism, that leads to an effective action, which is invariant under all the three differentials of the Sp(3) algebra, is given.

Minimal Free Multi-Models for Chain Algebras

2004 ◽  
Vol 11 (4) ◽  
pp. 733-752 ◽  
Author(s):  
J. Huebschmann
Keyword(s):  
Perturbation Theory ◽  
Local Ring ◽  
Minimal Model ◽  
Graded Algebra ◽  
Differential Graded Algebra ◽  
Homological Perturbation Theory ◽  
Homological Perturbation

Abstract Let 𝑅 be a local ring and 𝐴 a connected differential graded algebra over 𝑅 which is free as a graded 𝑅-module. Using homological perturbation theory techniques, we construct a minimal free multi-model for 𝐴 having properties similar to those of an ordinary minimal model over a field; in particular the model is unique up to isomorphism of multialgebras. The attribute ‘multi’ refers to the category of multicomplexes.

Sign in / Sign up

Export Citation Format

Share Document