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  • 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.
  • 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. (en)
Title
  • A generalization of Thom's transversality theorem
  • A generalization of Thom's transversality theorem (en)
skos:prefLabel
  • A generalization of Thom's transversality theorem
  • A generalization of Thom's transversality theorem (en)
skos:notation
  • RIV/00216224:14310/08:00025371!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/05/2117), Z(MSM0021622409)
http://linked.open...iv/cisloPeriodika
  • 5
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 354202
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14310/08:00025371
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • transversality; residual; generic; restriction; fibrewise singularity (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [89446EC091F4]
http://linked.open...i/riv/nazevZdroje
  • Archivum Mathematicum
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 44
http://linked.open...iv/tvurceVysledku
  • Vokřínek, Lukáš
http://linked.open...n/vavai/riv/zamer
issn
  • 0044-8753
number of pages
http://localhost/t...ganizacniJednotka
  • 14310
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