Cobordism of singular maps
| dc.creator | Szűcs, András | |
| dc.date | 2006-12-06 | |
| dc.date | 2008-07-28 | |
| dc.date.accessioned | 2026-07-07T09:53:01Z | |
| dc.date.available | 2026-07-07T09:53:01Z | |
| dc.description | We prove a conjecture due to M. Kazarian, connecting two classifying spaces in singularity theory. These spaces are: - Kazarian's space (generalizing Vassiliev's algebraic complex and) showing which cohomology classes are represented by singularity strata. - Author's space $X_τ$ giving homotopy representation of cobordisms of singular maps with a given list of allowed singularities \cite{R--Sz}. As a consequence we obtain the ranks of cobordism groups of singular maps with a given list of allowed singularities, and also their $p$-torsion parts for big primes $p.$ Further we give complete answer to the problem of elimination of singularities by cobordisms. Obtain very clear homotopical description of the classifying space $X_τ.$ We reveal some connection of the torsion parts of these cobordism groups to the stable homotopy groups of spheres and values of Thom polynomials. | |
| dc.description | Revised version, some parts were excluded, some parts are explained in greater detail | |
| dc.identifier | https://arxiv.org/abs/math/0612152 | |
| dc.identifier | http://arxiv.org/abs/math/0612152 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165804 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57R45; 55P42 | |
| dc.title | Cobordism of singular maps | |
| dc.type | text |