• norsk
    • English
  • English 
    • norsk
    • English
  • Login
View Item 
  •   Home
  • Fakultet for informasjonsteknologi og elektroteknikk (IE)
  • Institutt for matematiske fag
  • View Item
  •   Home
  • Fakultet for informasjonsteknologi og elektroteknikk (IE)
  • Institutt for matematiske fag
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

A classifying space for principal G-bundles with connection, in the category of simplicial presheaves

Flydal, Peter Marius
Master thesis
Thumbnail
View/Open
no.ntnu:inspera:2453820.pdf (7.115Mb)
URI
http://hdl.handle.net/11250/2622841
Date
2019
Metadata
Show full item record
Collections
  • Institutt for matematiske fag [2673]
Abstract
I denne masteroppgaven studerer vi hoved-G-bunter over glatte mangfoldigheter med kobling, og hvordan man kan lage universelle objekter for å klassifisere dem, tilsvarende Grassmannians for vektorbunter. Konstruksjonene tar oss inn i kategorien av simplisielle preknipper over glatte mangfoldigheter, og resulterer i et teorem som sier at de eneste naturlige differensialformene assosiert med koblingen på hoved-G-bunter er de man konstruerer med Chern-Weil-homomorfien. Dette ble først gjort av Freed og Hopkins i [7]. I siste kapittel tar vi en liten kikk på hva som ville skjedd hvis mangfoldighetene vi jobbet med var komplekse i steden for glatte.
 
In this master's thesis, we study principal G-bundles on smooth manifolds with connection, and how to make universal objects to classify them, similar to Grassmannians for vector bundles. The constructions take us into the category of simplicial presheaves on smooth manifolds, and result in a theorem that states that the only natural differential forms associated to the connection on principal G-bundles are the ones constructed in the Chern-Weil homomorphism. This was first obtained in this way by Freed and Hopkins in [7]. In the last chapter, we take a short look at what would happen if the manifolds considered were complex instead of smooth.
 
Publisher
NTNU

Contact Us | Send Feedback

Privacy policy
DSpace software copyright © 2002-2019  DuraSpace

Service from  Unit
 

 

Browse

ArchiveCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsDocument TypesJournalsThis CollectionBy Issue DateAuthorsTitlesSubjectsDocument TypesJournals

My Account

Login

Statistics

View Usage Statistics

Contact Us | Send Feedback

Privacy policy
DSpace software copyright © 2002-2019  DuraSpace

Service from  Unit