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On the perturbation lemma, and deformations
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On the perturbation lemma, and deformations
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We have one more look at the (homological) perturbation lemma and we point out some non-standard consequences, including the relevance to deformations.
Forward citations
Cited by 7 Pith papers
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Globalization of perturbative Chern-Simons theory on the moduli space of flat connections in the BV formalism
Perturbative Chern-Simons theory is globalized over the moduli space of flat connections in the BV formalism, yielding a cohomology class that defines a metric-independent 3-manifold invariant.
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BV pushforward as a quasi-isomorphism
Proves the BV pushforward is a quasi-isomorphism of BV complexes via homological perturbation lemma and gives a path integral formula for its quasi-inverse.
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Fat Lie Theory
Fat Lie theory defines fat extensions and abstract 2-term ruths with one-to-one correspondences to general linear PB-groupoids and core-transitive double groupoids, upgrading prior equivalences to category equivalences.
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Homotopy transfer for massive Kaluza-Klein modes
An algorithm based on homotopy transfer in L∞ algebras produces gauge-invariant fields for massive Kaluza-Klein modes that remain covariant under unbroken zero-mode gauge transformations.
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Minimal resolutions of toric substacks by line bundles
Minimal resolutions of toric substack structure sheaves are built as deformation retracts of cellular resolutions with explicit combinatorial differentials via the homological perturbation lemma and Moore-Penrose inverses.
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Field theory of $\mathfrak{su}(n)$: the absence of non-zero scatterings
The authors prove the absence of non-zero trivalent tree-level scattering amplitudes in su(n) field theory toy models via homological perturbation theory and demonstrate non-trivial higher products in an enlarged field space.
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Forms, half-densities, and the quantum odd symplectic category in the BV formalism
Reviews the geometry of forms and half-densities in the Batalin-Vilkovisky formalism and its relation to the quantum odd symplectic category.
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