Central extensions of mapping class groups from characteristic classes

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Central extensions of mapping class groups from characteristic classes
Original language description
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.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical
Cahiers de Topologie et Géométrie Différentielle Catégoriques
ISSN
1245-530X
e-ISSN
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Volume of the periodical
59
Issue of the periodical within the volume
3
Country of publishing house
FR - FRANCE
Number of pages
39
Pages from-to
260-298
UT code for WoS article
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EID of the result in the Scopus database
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