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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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