The *-holonomy group of the Stefan suspension of a diffeomorphism

• Autorzy: Andrzej Piątkowski
• Języki publikacji: EN

Abstrakty

EN

The definition of a Stefan suspension of a diffeomorphism is given. If $𝓖_g$ is the Stefan suspension of the diffeomorphism g over a Stefan foliation 𝓖, and G₀ ∈ 𝓖 satisfies the condition $g|G₀ = id_{G₀}$, then we compute the *-holonomy group for the leaf $F₀ ∈ 𝓖_g$ determined by G₀. A representative element of the *-holonomy along the standard imbedding of S¹ into F₀ is characterized. A corollary for the case when G₀ contains only one point is derived.

Słowa kluczowe

EN

Stefan foliation; suspension; holonomy group

Kategorie tematyczne

• 57R30: Foliations; geometric theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 2
• Strony: 123-129

Daty

wydano

1993

otrzymano

1992-02-15

poprawiono

1992-08-28

Twórcy

autor

Andrzej Piątkowski

• Institute of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [1] C. Ehresmann, Structures feuilletées, in: Proc. 5th Canad. Math. Congress, Montréal 1961, 109-172.
• [2] A. Piątkowski, A stability theorem for foliations with singularities, Dissertationes Math. 267 (1988).
• [3] A. Piątkowski, On the $*$-holonomy of the inverse image of a Stefan foliation, Acta Univ. Lodz. Folia Math., to appear.
• [4] P. Stefan, Accessible sets, orbits and foliations with singularities, Proc. London Math. Soc. 29 (1974), 699-713.
• [5] P. Ver Eecke, Le groupoïde fondamental d'un feuilletage de Stefan, Publ. Sem. Mat. García de Galdeano, Ser. II, Sec. 3, No. 6, Universidad de Zaragoza, 1986.