Strongly homotopy Lie algebras and deformations of calibrated submanifolds

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Strongly homotopy Lie algebras and deformations of calibrated submanifolds

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Strongly homotopy Lie algebras and deformations of calibrated submanifolds

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-00496S" target="_blank" >GA18-00496S: Singulární prostory ze speciální holonomie a foliací</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Asian Journal of Mathematics

ISSN

1093-6106

e-ISSN

1945-0036

Svazek periodika

25

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

341-368

Kód UT WoS článku

000771642400002

EID výsledku v databázi Scopus

2-s2.0-85126946761