Homology, Homotopy and Applications

Volume 18 (2016)

Number 1

Homotopy properties of some real algebraic maps

Pages: 287 – 294

DOI: https://dx.doi.org/10.4310/HHA.2016.v18.n1.a15


Maciej Zieliński (Institute of Mathematics, Jagiellonian University, Kraków, Poland)


We generalize an old result concerning homotopy groups of regular maps between a compact real algebraic variety and a Grassmann variety to a recently introduced class of stratified-regular maps. More precisely, we show that the embedding of the space of stratified-regular maps into the space of continuous (in the Euclidean topology) maps induces an isomorphism in all homotopy groups other then zeroth and a monomorphism in the latter case.


algebraic vector bundle, stratified-regular map, Grassmannian

2010 Mathematics Subject Classification

14P05, 14P25

Published 31 May 2016