홈 editorial content online
Volume 14 (2012)
No 1
Volume 13 (2011)
No 1
Volume 12 (2010)
No 1
Volume 11 (2009)
No 1, No 2
Volume 10 (2008)
No 1, No 2
Volume 9 (2006)
No 1, No 2
Volume 8 (2005)
No 1, No 2
Volume 7 (2004)
No 1, No 2
Volume 6 (2003)
No 1, No 2
Volume 5 (2002)
No 1, No 2
Volume 4 (2001)
No 1, No 2
Volume 3 (2000)
No 1
Volume 2 (1999)
No 1
Volume 1 (1998)
No 1

(1999 / vol.2 / no.1)
Algebraic and Nash Structures of $C^infty G$ manifolds, and Definable $G$ Manifolds in an $O$-minimal Exponsion of $(Bbb{R}, +, cdot, <)$
Tomohiro Kawakami
Pages. 10-18     



The purpose of this article is an overview of results obtained as
a part of a program to develop transformation groups in the algebraic, Nash,
and definable category. The emphasis is on the algebraic and Nash realization of
equivariant manifolds, and on the equivariant definable manifolds in
$o$-minimal expansion of $(Bbb{R}, + , cdot, <)$. Finally, we make some question related
to the subject.



1. Introduction
2. Definable $G$ manifolds and Nash $G$ manifolds
3. Results
4. Sketches of proofs
5. Questions



$C^inftyG$ manifolds, Nash $G$ manifolds, definable $C^omega G$ manifolds, $o$-minimal, nonsingular algebraic sets



14P10, 14P15, 14P20, 57S05, 57