Strongly homotopy Lie algebras and deformations of calibrated submanifolds
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00555439" target="_blank" >RIV/67985840:_____/21:00555439 - isvavai.cz</a>
Result on the web
<a href="https://dx.doi.org/10.4310/AJM.2021.v25.n3.a2" target="_blank" >https://dx.doi.org/10.4310/AJM.2021.v25.n3.a2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4310/AJM.2021.v25.n3.a2" target="_blank" >10.4310/AJM.2021.v25.n3.a2</a>
Alternative languages
Result language
angličtina
Original language name
Strongly homotopy Lie algebras and deformations of calibrated submanifolds
Original language description
For an element Ψ in the graded vector space Ω∗(M,TM) of tangent bundle valued forms on a smooth manifold M, a Ψ-submanifold is defined as a submanifold N of M such that Ψ|N∈Ω∗(N,TN). The class of Ψ-submanifolds encompasses calibrated submanifolds, complex submanifolds and all Lie subgroups in compact Lie groups. The graded vector space Ω∗(M,TM) carries a natural graded Lie algebra structure, given by the Frölicher–Nijenhuis bracket [−,−]FN. When Ψ is an odd degree element with [Ψ,Ψ]FN=0, we associate to a Ψ-submanifold N a strongly homotopy Lie algebra, which governs the formal and (under certain assumptions) smooth deformations of N as a Ψ-submanifold, and we show that under certain assumptions these deformations form an analytic variety. As an application we revisit formal and smooth deformation theory of complex closed submanifolds and of φ-calibrated closed submanifolds, where φ is a parallel form in a real analytic Riemannian manifold.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-00496S" target="_blank" >GA18-00496S: Singular spaces from special holonomy and foliations</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Asian Journal of Mathematics
ISSN
1093-6106
e-ISSN
1945-0036
Volume of the periodical
25
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
28
Pages from-to
341-368
UT code for WoS article
000771642400002
EID of the result in the Scopus database
2-s2.0-85126946761