| Title:
|
A generalization of Thom’s transversality theorem (English) |
| Author:
|
Vokřínek, Lukáš |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
5 |
| Year:
|
2008 |
| Pages:
|
523-533 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove a generalization of Thom’s transversality theorem. It gives conditions under which the jet map $f_*|_Y\colon Y\subseteq J^r(D,M)\rightarrow J^r(D,N)$ is generically (for $f\colon M\rightarrow N$) transverse to a submanifold $Z\subseteq J^r(D,N)$. We apply this to study transversality properties of a restriction of a fixed map $g\colon M\rightarrow P$ to the preimage $(j^sf)^{-1}(A)$ of a submanifold $A\subseteq J^s(M,N)$ in terms of transversality properties of the original map $f$. Our main result is that for a reasonable class of submanifolds $A$ and a generic map $f$ the restriction $g|_{(j^sf)^{-1}(A)}$ is also generic. We also present an example of $A$ where the theorem fails. (English) |
| Keyword:
|
transversality |
| Keyword:
|
residual |
| Keyword:
|
generic |
| Keyword:
|
restriction |
| Keyword:
|
fibrewise singularity |
| MSC:
|
57R35 |
| MSC:
|
57R45 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 1212.57010 |
| idMR:
|
MR2501582 |
| . |
| Date available:
|
2009-01-29T09:16:29Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127118 |
| . |
| Reference:
|
[1] Golubitsky, M., Guillemin, V.: Stable mappings and their singularities.Grad. Texts in Math., Vol. 14, Springer-Verlag, New York-Heidelberg, 1973. Zbl 0294.58004, MR 0341518, 10.1007/978-1-4615-7904-5 |
| Reference:
|
[2] Hirsch, M. W.: Differential topology.Grad. Texts in Math., No. 33, Springer-Verlag, New York-Heidelberg, 1976. Zbl 0356.57001, MR 0448362 |
| . |
