On coincidences of Morin and first order Thom-Boardman singular loci
András Csépai, András Szűcs, and Tamás Terpai
Journal of Singularities
volume 27 (2024), 149-166
Received: 24 March 2024.
Abstract:
It is well-known that the Thom polynomial in Stiefel--Whitney classes expressing the cohomology class dual to the locus of the cusp singularity for codimension-k maps and that of the corank-2 singularity for codimension-(k-1) maps coincide. The aim of the present paper is to find out whether there is any geometric explanation to this seemingly mysterious coincidence. We thank László Fehér for posing us this interesting question that we answer here in the positive, and motivated by it we search for further similar coincidences of the loci of the corank-r and Morin singular points, but found such only for special classes of maps. Finally we compute the cohomology classes dual to the singularity strata for any Morin map. (This result-for holomorphic maps-was presented by Kazarian but the proof was left unpublished.)
2020 Mathematical Subject Classification:
57R45 (Primary); 57R70; 57R20 (Secondary)
Key words and phrases:
Thom polynomials; relation of singular loci
Author(s) information:
András Csépai
ELTE Eötvös Loránd University
Budapest, Hungary
Institute of Mathematics
Pázmány Péter sétány 1/c
Budapest, H-1117 Hungary
email: csepai.andras112358@gmail.com
András Szűcs
ELTE Eötvös Loránd University
Budapest, Hungary
Institute of Mathematics
Pázmány Péter sétány 1/c
Budapest, H-1117 Hungary
email: andras.szucs@ttk.elte.hu
Tamás Terpai
ELTE Eötvös Loránd University
Budapest, Hungary
Institute of Mathematics
Pázmány Péter sétány 1/c
Budapest, H-1117 Hungary
email: terpai@math.elte.hu