Removal of singularities through hierarchies of singularities

Abstract

In this thesis we consider a removal of singularities proof for the Smale-Hirsch theorem about immersions in the non-critical dimension case. This proof was suggested by M. Gromov in his book Partial Differential Relations. In this thesis we present a reconstruction of the argument described by Gromov and provide full details for it. In particular, we present a general construction of hierarchies of singularities in jet spaces of sections, which are based on theThom-Boardman singularities for jet spaces of functions.