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@article{839482,
author = {Vokřínek, Lukáš},
article_location = {Brno},
article_number = {5},
keywords = {transversality; residual; generic; restriction; fibrewise singularity},
language = {eng},
issn = {0044-8753},
journal = {Archivum Mathematicum},
title = {A generalization of Thom's transversality theorem},
volume = {44},
year = {2008}
}
TY - JOUR
ID - 839482
AU - Vokřínek, Lukáš
PY - 2008
TI - A generalization of Thom's transversality theorem
JF - Archivum Mathematicum
VL - 44
IS - 5
SP - 523-533
EP - 523-533
PB - Masaryk University
SN - 00448753
KW - transversality
KW - residual
KW - generic
KW - restriction
KW - fibrewise singularity
N2 - We prove a generalization of Thom's transversality theorem. It gives conditions under which the restriction f_*|_Y:Y->J^r(D,M)->J^r(D,N) of the jet map induced by f:M->N is generically transverse to a submanifold Z of the target. We apply this to study transversality properties of a restriction of a fixed map g to the preimage (j^sf)^{-1}(A) of a submanifold A of 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 of g is also generic. We also present an example of A for which an analogous statement would fail.
ER -
VOKŘÍNEK, Lukáš. A generalization of Thom's transversality theorem. \textit{Archivum Mathematicum}. Brno: Masaryk University, 2008, vol.~44, No~5, p.~523-533. ISSN~0044-8753.
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