homological perturbation
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2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Christian Saemann ◽  
Emmanouil Sfinarolakis

Abstract We discuss the symmetry factors of Feynman diagrams of scalar field theories with polynomial potential. After giving a concise general formula for them, we present an elementary and direct proof that when computing scattering amplitudes using the homological perturbation lemma, each contributing Feynman diagram is indeed included with the correct symmetry factor.


Author(s):  
Graham Ellis

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.


Author(s):  
Graham Ellis

This chapter introduces the basic ingredients of the cohomology of groups and describes datatypes and algorithms for implementing them on a computer. These are illustrated using computer examples involving: integral homology of finite groups such as the Mathieu groups, homology of crystallographic groups, homology of nilpotent groups, homology of Coxeter groups, transfer homomorphism, homological perturbation theory, mod-p comology rings of small finite p-groups, Lyndon-Hocshild-Serre spectral sequence, Bokstein operation, Steenrod squares, Stiefel-Whitney classes, Lie algebras, the modular isomorphism problem, and Bredon homology.


2019 ◽  
Vol 367 (1) ◽  
pp. 215-240 ◽  
Author(s):  
Martin Doubek ◽  
Branislav Jurčo ◽  
Ján Pulmann

2018 ◽  
Vol 25 (4) ◽  
pp. 603-622
Author(s):  
Francis Sergeraert

Abstract We propose in this article a global understanding of, on the one hand, the homological perturbation theorem (HPT) and, on the other hand, of Robin Forman’s theorems about the discrete vector fields (DVFs). Forman’s theorems become a simple and clear consequence of the HPT. Above both subjects, the homological hexagonal lemma quite elementary.


2018 ◽  
Vol 25 (4) ◽  
pp. 529-544 ◽  
Author(s):  
Johannes Huebschmann

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.


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