Let Y be a compact nonsingular real algebraic set whose homology classes (over Z/2) are represented by Zariski closed subsets. It is well known that every smooth map from a compact smooth manifold to Y is unoriented bordant to a regular map. In this paper, we show how to construct smooth maps from compact nonsingular real algebraic sets to Y not homotopic to any regular map starting from a nonzero homology class of Y of positive degree. We use these maps to obtain obstructions to the existence of local algebraic tubular neighborhoods of algebraic submanifolds of R^n and to study some algebro-homological properties of rational real algebraic manifolds.
|Titolo:||Second order homological obstructions on real algebraic manifolds|
|Titolo del periodico:||TOPOLOGY AND ITS APPLICATIONS|
|Anno di pubblicazione:||2007|
|Numero e parte del fascicolo:||17|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/j.topol.2007.07.003|
|Appare nelle tipologie:||03.1 Articolo su rivista (Journal article)|