Publication details
A generalization of Thom's transversality theorem
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Article in Periodical |
| Magazine / Source | Archivum Mathematicum |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | transversality; residual; generic; restriction; fibrewise singularity |
| Description | 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. |
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