On the rigidity of webs

Michel Belliart

Bulletin de la Société Mathématique de France (2007)

  • Volume: 135, Issue: 1, page 1-24
  • ISSN: 0037-9484

Abstract

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Plane d -webs have been studied a lot since their appearance at the turn of the 20th century. A rather recent and striking result for them is the theorem of Dufour, stating that the measurable conjugacies between 3-webs have to be analytic. Here, we show that even the set-theoretic conjugacies between two d -webs, d ≥ 3 are analytic unless both webs are analytically parallelizable. Between two set-theoretically conjugate parallelizable d -webs, however, there always exists a nonmeasurable conjugacy; still, every pair of set-theoretically conjugate 3 -webs (parallelizable or not) also are analytically conjugate, while if d ≥ 4 there exist pairs of d -webs which are set-theoretically conjugate but not even measurably so.

How to cite

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Belliart, Michel. "On the rigidity of webs." Bulletin de la Société Mathématique de France 135.1 (2007): 1-24. <http://eudml.org/doc/272367>.

@article{Belliart2007,
abstract = {Plane $d$-webs have been studied a lot since their appearance at the turn of the 20th century. A rather recent and striking result for them is the theorem of Dufour, stating that the measurable conjugacies between 3-webs have to be analytic. Here, we show that even the set-theoretic conjugacies between two $d$-webs, $d\ge 3$ are analytic unless both webs are analytically parallelizable. Between two set-theoretically conjugate parallelizable $d$-webs, however, there always exists a nonmeasurable conjugacy; still, every pair of set-theoretically conjugate $3$-webs (parallelizable or not) also are analytically conjugate, while if $d\ge 4$ there exist pairs of $d$-webs which are set-theoretically conjugate but not even measurably so.},
author = {Belliart, Michel},
journal = {Bulletin de la Société Mathématique de France},
keywords = {foliations; 3-webs; conjugacy; rigidity},
language = {eng},
number = {1},
pages = {1-24},
publisher = {Société mathématique de France},
title = {On the rigidity of webs},
url = {http://eudml.org/doc/272367},
volume = {135},
year = {2007},
}

TY - JOUR
AU - Belliart, Michel
TI - On the rigidity of webs
JO - Bulletin de la Société Mathématique de France
PY - 2007
PB - Société mathématique de France
VL - 135
IS - 1
SP - 1
EP - 24
AB - Plane $d$-webs have been studied a lot since their appearance at the turn of the 20th century. A rather recent and striking result for them is the theorem of Dufour, stating that the measurable conjugacies between 3-webs have to be analytic. Here, we show that even the set-theoretic conjugacies between two $d$-webs, $d\ge 3$ are analytic unless both webs are analytically parallelizable. Between two set-theoretically conjugate parallelizable $d$-webs, however, there always exists a nonmeasurable conjugacy; still, every pair of set-theoretically conjugate $3$-webs (parallelizable or not) also are analytically conjugate, while if $d\ge 4$ there exist pairs of $d$-webs which are set-theoretically conjugate but not even measurably so.
LA - eng
KW - foliations; 3-webs; conjugacy; rigidity
UR - http://eudml.org/doc/272367
ER -

References

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