Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Differentiable structures on function spaces


Author: Nishan Krikorian
Journal: Trans. Amer. Math. Soc. 171 (1972), 67-82
MSC: Primary 58D15; Secondary 58B10
MathSciNet review: 0312525
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A $ {C^s}$ differentiable manifold structure is constructed for spaces of maps from a compact $ {C^r}$ manifold $ M$ to a $ {C^{r + s}}$ manifold $ N$. The method (1) is inspired by Douady; (2) does not require any additional structure on $ N$ (such as sprays); (3) includes the case when $ N$ is an analytic manifold and concludes that the mapping space is also an analytic manifold; (4) can be used to treat all the classical mapping spaces ($ {C^r}$ functions, $ {C^r}$ functions with Hölder conditions, and Sobolev functions). Several interesting aspects of these manifolds are investigated such as their tangent spaces, their behavior with respect to functions, and realizations of Lie group structures on them. Differentiable structures are also exhibited for spaces of compact maps with noncompact domain.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58D15, 58B10

Retrieve articles in all journals with MSC: 58D15, 58B10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0312525-5
PII: S 0002-9947(1972)0312525-5
Keywords: Differentiable structure, Banach manifold, exponential map, manifold model, differential map, analytic map, submersion, fibre product, transversal pair, Banach Lie group, foliation, Whitney extension, Hölder condition, Sobolev spaces, Calderón extension, compact map, Dugundji extension
Article copyright: © Copyright 1972 American Mathematical Society