Deutsch
 
Hilfe Datenschutzhinweis Impressum
  DetailsucheBrowse

Datensatz

DATENSATZ AKTIONENEXPORT

Freigegeben

Zeitschriftenartikel

A framework for geometric field theories and their classification in dimension one

MPG-Autoren
/persons/resource/persons235730

Ludewig,  Matthias
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons240188

Stoffel,  Augusto
Max Planck Institute for Mathematics, Max Planck Society;

Externe Ressourcen
Volltexte (beschränkter Zugriff)
Für Ihren IP-Bereich sind aktuell keine Volltexte freigegeben.
Ergänzendes Material (frei zugänglich)
Es sind keine frei zugänglichen Ergänzenden Materialien verfügbar
Zitation

Ludewig, M., & Stoffel, A. (2021). A framework for geometric field theories and their classification in dimension one. Symmetry, Integrability and Geometry: Methods and Applications, 17: 072. doi:10.3842/SIGMA.2021.072.


Zitierlink: https://hdl.handle.net/21.11116/0000-0009-B90A-C
Zusammenfassung
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such geometric structures, so that it makes sense to require the output of our field theory to depend smoothly on the input. We then test our framework on the case of 1-dimensional field theories (with or without orientation) over a manifold M. Here the expectation is that such a field theory is equivalent to the data of a vector bundle over M with connection and, in the nonoriented case, the additional data of a nondegenerate bilinear pairing; we prove that this is indeed the case in our framework.