Preservation of Immersed or Injective Properties by Composing Generic Generalized Distance-Squared Mappings

Ichiki, Shunsuke; Nishimura, Takashi

doi:10.1007/978-3-319-73639-6_18

Cited by 2 publications

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“…3. The essential idea for the proofs of Theorems 1 and 2 is to apply Lemma 1, and it is almost similar to the idea of the proofs of main results in [8]. Nevertheless, the two main theorems in this paper are drastically improved.…”

Section: For Any Injectionmentioning

confidence: 95%

Composing generic linearly perturbed mappings and immersions/injections

Ichiki¹

2018

J. Math. Soc. Japan

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Let N (resp., U ) be a manifold (resp., an open subset of R m ). Let f : N → U and F : U → R ℓ be an immersion and a C ∞ mapping, respectively. Generally, the composition F • f does not necessarily yield a mapping transverse to a given subfiber-bundle of J 1 (N, R ℓ ). Nevertheless, in this paper, for any A 1 -invariant fiber, we show that composing generic linearly perturbed mappings of F and the given immersion f yields a mapping transverse to the subfiber-bundle of J 1 (N, R ℓ ) with the given fiber. Moreover, we show a specialized transversality theorem on crossings of compositions of generic linearly perturbed mappings of a given mapping F : U → R ℓ and a given injection f : N → U . Furthermore, applications of the two main theorems are given.

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