Almost formality of manifolds of low dimension
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00541715" target="_blank" >RIV/67985840:_____/21:00541715 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.2422/2036-2145.201905_002" target="_blank" >https://doi.org/10.2422/2036-2145.201905_002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2422/2036-2145.201905_002" target="_blank" >10.2422/2036-2145.201905_002</a>
Alternative languages
Result language
angličtina
Original language name
Almost formality of manifolds of low dimension
Original language description
In this paper we introduce the notion of Poincar'e DGCAs of Hodge type, which is a subclass of Poincar'e DGCAs encompassing the de Rham algebras of closed orientable manifolds. Then we introduce the notion of the small algebra and the small quotient algebra of a Poincar'e DGCA of Hodge type. Using these concepts, we investigate the equivalence class of $(r-1)$ connected $(r>1)$ Poincar'e DGCAs of Hodge type. In particular, we show that a $(r-1)$ connected Poincar'e DGCA of Hodge type $Aa^ast$ of dimension $n le 5r-3$ is $A_infty$-quasi-isomorphic to an $A_3$-algebra and prove that the only obstruction to the formality of $Aa^ast$ is a distinguished Harrison cohomology class $[mu_3] in {mathsf{Harr}}^{3,-1} (H^*(Aa^ast), H^*(Aa^ast))$. Moreover, the cohomology class $[mu_3]$ and the DGCA isomorphism class of $H^*(Aa^ast)$ determine the $A_infty$-quasi-isomorphism class of $Aa^ast$.
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
—
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
Scuola Normale Superiore di Pisa. Annali. Classe di Scienze
ISSN
0391-173X
e-ISSN
2036-2145
Volume of the periodical
22
Issue of the periodical within the volume
1
Country of publishing house
IT - ITALY
Number of pages
29
Pages from-to
79-107
UT code for WoS article
000709769600004
EID of the result in the Scopus database
2-s2.0-85117899740