Mathematics – Geometric Topology
Scientific paper
2009-10-16
Mathematics
Geometric Topology
Scientific paper
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 see [ABB]. Finally we deduce the validity of the semialgebraic and Nash versions of these theorems over any real closed field.
No associations
LandOfFree
h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash categories, Uniform bound and Effectiveeness does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash categories, Uniform bound and Effectiveeness, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash categories, Uniform bound and Effectiveeness will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-124436