Homology reduction of cycles in the complement of an algebraic hypersurface
N A Buruchenko, Avgust Karlovich Tsikh · Sbornik Mathematics · 1995
An example of a 3-dimensional cycle in the complement of an algebraic hypersurface that cannot be deformed into a tube over (is not homologous to the coboundary of) a 2-dimensional cycle in the set of regular points of is presented. Thus, the corresponding result of Poincare in fails in for 2$ SRC=http://ej.iop.org/images/1064-5616/186/10/A02/tex_sm_76_img5.gif/>. It is proved that Poincare's result holds for hypersurfaces in with a 'thin' set of singularities that are complete intersections.