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

Andrzej Piątkowski

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 2, page 123-129
  • ISSN: 0066-2216

Abstract

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The definition of a Stefan suspension of a diffeomorphism is given. If g is the Stefan suspension of the diffeomorphism g over a Stefan foliation , and G₀ ∈ satisfies the condition g | G ₀ = i d G ₀ , then we compute the *-holonomy group for the leaf F ₀ ∈ 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.

How to cite

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Andrzej Piątkowski. "The *-holonomy group of the Stefan suspension of a diffeomorphism." Annales Polonici Mathematici 58.2 (1993): 123-129. <http://eudml.org/doc/262509>.

@article{AndrzejPiątkowski1993,
abstract = {The definition of a Stefan suspension of a diffeomorphism is given. If $_g$ is the Stefan suspension of the diffeomorphism g over a Stefan foliation , and G₀ ∈ satisfies the condition $g|G₀ = id_\{G₀\}$, then we compute the *-holonomy group for the leaf $F₀ ∈ _g$ 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.},
author = {Andrzej Piątkowski},
journal = {Annales Polonici Mathematici},
keywords = {Stefan foliation; suspension; holonomy group; suspending a singular foliation},
language = {eng},
number = {2},
pages = {123-129},
title = {The *-holonomy group of the Stefan suspension of a diffeomorphism},
url = {http://eudml.org/doc/262509},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Andrzej Piątkowski
TI - The *-holonomy group of the Stefan suspension of a diffeomorphism
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 2
SP - 123
EP - 129
AB - The definition of a Stefan suspension of a diffeomorphism is given. If $_g$ is the Stefan suspension of the diffeomorphism g over a Stefan foliation , and G₀ ∈ satisfies the condition $g|G₀ = id_{G₀}$, then we compute the *-holonomy group for the leaf $F₀ ∈ _g$ 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.
LA - eng
KW - Stefan foliation; suspension; holonomy group; suspending a singular foliation
UR - http://eudml.org/doc/262509
ER -

References

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  1. [1] C. Ehresmann, Structures feuilletées, in: Proc. 5th Canad. Math. Congress, Montréal 1961, 109-172. 
  2. [2] A. Piątkowski, A stability theorem for foliations with singularities, Dissertationes Math. 267 (1988). Zbl1003.57500
  3. [3] A. Piątkowski, On the * -holonomy of the inverse image of a Stefan foliation, Acta Univ. Lodz. Folia Math., to appear. Zbl0832.57016
  4. [4] P. Stefan, Accessible sets, orbits and foliations with singularities, Proc. London Math. Soc. 29 (1974), 699-713. Zbl0342.57015
  5. [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. Zbl0607.57019

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