Induced differential forms on manifolds of functions

Cornelia Vizman

Archivum Mathematicum (2011)

  • Volume: 047, Issue: 3, page 201-215
  • ISSN: 0044-8753

Abstract

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Differential forms on the Fréchet manifold ℱ ( S , M ) of smooth functions on a compact k -dimensional manifold S can be obtained in a natural way from pairs of differential forms on M and S by the hat pairing. Special cases are the transgression map Ω p ( M ) → Ω p - k ( ℱ ( S , M ) ) (hat pairing with a constant function) and the bar map Ω p ( M ) → Ω p ( ℱ ( S , M ) ) (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].

How to cite

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Vizman, Cornelia. "Induced differential forms on manifolds of functions." Archivum Mathematicum 047.3 (2011): 201-215. <http://eudml.org/doc/247143>.

@article{Vizman2011,
abstract = {Differential forms on the Fréchet manifold $\mathcal \{F\}(S,M)$ of smooth functions on a compact $k$-dimensional manifold $S$ can be obtained in a natural way from pairs of differential forms on $M$ and $S$ by the hat pairing. Special cases are the transgression map $\Omega ^p(M)\rightarrow \Omega ^\{p-k\}(\mathcal \{F\}(S,M))$ (hat pairing with a constant function) and the bar map $\Omega ^p(M)\rightarrow \Omega ^p(\mathcal \{F\}(S,M))$ (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].},
author = {Vizman, Cornelia},
journal = {Archivum Mathematicum},
keywords = {manifold of functions; fiber integral; diffeomorphism group; manifold of functions; fiber integral; diffeomorphism group},
language = {eng},
number = {3},
pages = {201-215},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Induced differential forms on manifolds of functions},
url = {http://eudml.org/doc/247143},
volume = {047},
year = {2011},
}

TY - JOUR
AU - Vizman, Cornelia
TI - Induced differential forms on manifolds of functions
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 3
SP - 201
EP - 215
AB - Differential forms on the Fréchet manifold $\mathcal {F}(S,M)$ of smooth functions on a compact $k$-dimensional manifold $S$ can be obtained in a natural way from pairs of differential forms on $M$ and $S$ by the hat pairing. Special cases are the transgression map $\Omega ^p(M)\rightarrow \Omega ^{p-k}(\mathcal {F}(S,M))$ (hat pairing with a constant function) and the bar map $\Omega ^p(M)\rightarrow \Omega ^p(\mathcal {F}(S,M))$ (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].
LA - eng
KW - manifold of functions; fiber integral; diffeomorphism group; manifold of functions; fiber integral; diffeomorphism group
UR - http://eudml.org/doc/247143
ER -

References

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