The homotopy principle for maps with singularities of given K-invariant class

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概要

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• Let N and P be smooth manifolds of dimensions n and p respectively such that n≥p≥2 or n<p. Let $\mathscr{O}$(N,P) denote an open subspace of J∞(N,P) which consists of all regular jets and singular jets of certain given $\mathscr{K}$-invariant class (including fold jets if n≥p). An $\mathscr{O}$-regular map f:N→P refers to a smooth map such that j∞f(N)⊂\mathscr{O}(N,P). We will prove that a continuous section s of $\mathscr{O}$(N,P) over N has an $\mathscr{O}$-regular map f such that s and j∞f are homotopic as sections. As an application we will prove this homotopy principle for maps with $\mathscr{K}$-simple singularities of given class.

• 社団法人 日本数学会の論文
• 2007-04-01

著者

• Ando Yoshifumi

  Department Of Mathematical Sciences Faculty Of Science Yamaguchi University

関連論文

• Folding maps and the surgery theory on manifolds
• On the Higher Thom Polynomials of Morin Singularities : Dedicated to Professor H. Toda on his 60th birthday
• Existence theorems of fold-maps
• Elimination of certain Thom-Boardman singularities of order two
• The homotopy principle for maps with singularities of given K-invariant class
• Invariants of Fold-maps via Stable Homotopy Groups : Dedicated to Professor Tatsuo Suwa on his sixtieth birthday
• The homotopy type of the space consisting of regular jets and folding jets in J^2 (n, n)
• On thom polynomials of the singularities D_k nad E_k

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