2016/12/04 by Shunsuke Ichiki, Ichiki, Shunsuke · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.GT #msc:57R42 #msc:57R45
paper · pdf · doi:10.48550/arxiv.1612.01100
19 pages. Accepted for publication in Journal of the Mathematical Society of Japan. The paper is a generalization of arXiv:1610.02880. As the appendix, the statement of the main theorem in arXiv:1607.03220 (the proof of it is in arXiv:1607.03220) is introduced in the final section of this paper
arxiv created 2017/12/25 · arxiv updated 2017/12/27
Let N (resp., U) be a manifold (resp., an open subset of ℝm). 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 J1(N,ℝ^ℓ). Nevertheless, in this paper, for any A1-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 J1(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.