Page 1 Next

Displaying 1 – 20 of 39

Showing per page

A note on global Nash subvarieties and Artin-Mazur theorem

Alessandro Tancredi, Alberto Tognoli (2004)

Bollettino dell'Unione Matematica Italiana

It is shown that every connected global Nash subvariety of R n is Nash isomorphic to a connected component of an algebraic variety that, in the compact case, can be chosen with only two connected components arbitrarily near each other. Some examples which state the limits of the given results and of the used tools are provided.

Classification of Nash manifolds

Masahiro Shiota (1983)

Annales de l'institut Fourier

A semi-algebraic analytic manifold and a semi-algebraic analytic map are called a Nash manifold and a Nash map respectively. We clarify the category of Nash manifolds and Nash maps.

Extending algebraic actions.

Arthur G. Wasserman (1999)

Revista Matemática Complutense

There is a well-known procedure -induction- for extending an action of a subgroup H of a Lie group G on a topological space X to an action of G on an associated space. Induction can also extend a smooth action of a subgroup H of a Lie group G on a manifold M to a smooth action of G on an associated manifold. In this paper elementary methods are used to show that induction also works in the category of (nonsingular) real algebraic varieties and regular or entire maps if G is a compact abelian Lie...

Faisceaux analytiques semi-cohérents

Jean Merrien (1980)

Annales de l'institut Fourier

Nous définissons deux notions nouvelles en géométrie analytique réelle, celle de fonction Nash-analytique et celle de faisceau semi-cohérent. Avec ces notions, nous obtenons des théorèmes de cohérence analogues à ceux du cas complexe (théorème de cohérence d’Oka, théorème de l’image directe, cohérence d’un ensemble analytique complexe).

Finiteness problems on Nash manifolds and Nash sets

José F. Fernando, José Manuel Gamboa, Jesús M. Ruiz (2014)

Journal of the European Mathematical Society

We study here several finiteness problems concerning affine Nash manifolds M and Nash subsets X . Three main results are: (i) A Nash function on a semialgebraic subset Z of M has a Nash extension to an open semialgebraic neighborhood of Z in M , (ii) A Nash set X that has only normal crossings in M can be covered by finitely many open semialgebraic sets U equipped with Nash diffeomorphisms ( u 1 , , u m ) : U m such that U X = { u 1 u r = 0 } , (iii) Every affine Nash manifold with corners N is a closed subset of an affine Nash manifold...

Modified Nash triviality of a family of zero-sets of real polynomial mappings

Toshizumi Fukui, Satoshi Koike, Masahiro Shiota (1998)

Annales de l'institut Fourier

In this paper we introduce the notion of modified Nash triviality for a family of zero sets of real polynomial map-germs as a desirable one. We first give a Nash isotopy lemma which is a useful tool to show triviality.Then, using it, we prove two types of modified Nash triviality theorem and a finite classification theorem for this triviality. These theorems strengthen similar topological results.

Nash Manifolds

Masahiro Shiota (1986)

Publications mathématiques et informatique de Rennes

Nash triviality in families of Nash mappings

Jesús Escribano (2001)

Annales de l’institut Fourier

We study triviality of Nash families of proper Nash submersions or, in a more general setting, the triviality of pairs of proper Nash submersions. We work with Nash manifolds and mappings defined over an arbitrary real closed field R . To substitute the integration of vector fields, we study the fibers of such families on points of the real spectrum R p ˜ and we construct models of proper Nash submersions over smaller real closed fields. Finally we obtain results on finiteness of topological types in...

Currently displaying 1 – 20 of 39

Page 1 Next