Central extensions of mapping class groups from characteristic classes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00499736" target="_blank" >RIV/67985840:_____/18:00499736 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Central extensions of mapping class groups from characteristic classes

Popis výsledku v původním jazyce

Tangential structures on smooth manifolds, and the extension of mapping class groups they induce, admit a natural formulation in terms of higher (stacky) differential geometry. This is the literal translation of a classical construction in differential topology to a sophisticated language, but it has the advantage of emphasizing how the whole construction naturally emerges from the basic idea of working in slice categories. We characterize, for every higher smooth stack equipped with tangential strukture, the induced higher group extension of the geometric realization of its higher automorphism stack. We shoe that when restricted to smooth manifolds equipped with higher degree topological structures, this produces higher extensions of homotopy types of diffeomorphism groups. Passing to the groups of connected components, we obtain abelian extensions of mapping class groups and we derive sufficient conditons for these being central.

Název v anglickém jazyce

Central extensions of mapping class groups from characteristic classes

Popis výsledku anglicky

Tangential structures on smooth manifolds, and the extension of mapping class groups they induce, admit a natural formulation in terms of higher (stacky) differential geometry. This is the literal translation of a classical construction in differential topology to a sophisticated language, but it has the advantage of emphasizing how the whole construction naturally emerges from the basic idea of working in slice categories. We characterize, for every higher smooth stack equipped with tangential strukture, the induced higher group extension of the geometric realization of its higher automorphism stack. We shoe that when restricted to smooth manifolds equipped with higher degree topological structures, this produces higher extensions of homotopy types of diffeomorphism groups. Passing to the groups of connected components, we obtain abelian extensions of mapping class groups and we derive sufficient conditons for these being central.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Cahiers de Topologie et Géométrie Différentielle Catégoriques

ISSN

1245-530X

e-ISSN

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Svazek periodika

59

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

39

Strana od-do

260-298

Kód UT WoS článku

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EID výsledku v databázi Scopus

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