h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness

Demdah Kartoue, Mady. "h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness." Annales de l’institut Fourier 61.4 (2011): 1573-1597. <http://eudml.org/doc/219827>.

@article{DemdahKartoue2011,
abstract = {The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nash cobordism data, we get a semialgebraic homeomorphism (respectively a Nash diffeomorphism). The main tools used are semialgebraic triangulation and Nash approximation.One aspect of the algebraic nature of semialgebraic or Nash objects is that one can measure their complexities. We show h and s-cobordism theorems with a uniform bound on the complexity of the semialgebraic homeomorphism (or Nash diffeomorphism) obtained in terms of the complexity of the cobordism data. The uniform bound of semialgebraic h-cobordism cannot be recursive, which gives another example of non effectiveness in real algebraic geometry. Finally we deduce the validity of the semialgebraic and Nash versions of these theorems over any real closed field.},
affiliation = {Université de Rennes 1 IRMAR (UMR CNRS 6625) Campus de Beaulieu 35042 Rennes cedex (France)},
author = {Demdah Kartoue, Mady},
journal = {Annales de l’institut Fourier},
keywords = {Cobordism; semialgebraic; complexity; effectiveness; cobordism},
language = {eng},
number = {4},
pages = {1573-1597},
publisher = {Association des Annales de l’institut Fourier},
title = {h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness},
url = {http://eudml.org/doc/219827},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Demdah Kartoue, Mady
TI - h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 4
SP - 1573
EP - 1597
AB - The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nash cobordism data, we get a semialgebraic homeomorphism (respectively a Nash diffeomorphism). The main tools used are semialgebraic triangulation and Nash approximation.One aspect of the algebraic nature of semialgebraic or Nash objects is that one can measure their complexities. We show h and s-cobordism theorems with a uniform bound on the complexity of the semialgebraic homeomorphism (or Nash diffeomorphism) obtained in terms of the complexity of the cobordism data. The uniform bound of semialgebraic h-cobordism cannot be recursive, which gives another example of non effectiveness in real algebraic geometry. Finally we deduce the validity of the semialgebraic and Nash versions of these theorems over any real closed field.
LA - eng
KW - Cobordism; semialgebraic; complexity; effectiveness; cobordism
UR - http://eudml.org/doc/219827
ER -