Translator Disclaimer
Summer 2014 On smooth locally o-minimal functions
Andreas Fischer
Illinois J. Math. 58(2): 285-309 (Summer 2014). DOI: 10.1215/ijm/1436275484

Abstract

We study the $\mathcal{C}^{\infty}$-smooth functions which are locally definable in an o-minimal expansion of the real exponential field with some additional smoothness conditions. Here, the local definability generalizes the subanalytic setting to more transcendental sets and functions. The focus is set on the locally definable diffeomorphisms between manifolds, for which we prove analogies to classical differential geometric results. Moreover, we investigate the relation between classical diffeomorphy and locally definable diffeomorphy.

Citation

Download Citation

Andreas Fischer. "On smooth locally o-minimal functions." Illinois J. Math. 58 (2) 285 - 309, Summer 2014. https://doi.org/10.1215/ijm/1436275484

Information

Received: 2 June 2012; Revised: 15 August 2012; Published: Summer 2014
First available in Project Euclid: 7 July 2015

zbMATH: 1325.32007
MathSciNet: MR3367649
Digital Object Identifier: 10.1215/ijm/1436275484

Subjects:
Primary: 14P10, 32B20
Secondary: 03C64, 26B05

Rights: Copyright © 2014 University of Illinois at Urbana-Champaign

JOURNAL ARTICLE
25 PAGES


SHARE
Vol.58 • No. 2 • Summer 2014
Back to Top