Read e-book online 1-formes ferm6es singuli6res et groupe fondamental PDF

By Levitt G.

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Soit co une forme dent le lieu singulier est de codimension au moins 3. On suppose que co est de rang au moins 2, et que Ice]: ) h M - ~ I R ne se factorise pas de f a f o n non triviale par un 7la*7I b. 1). Remarque. Ce th6or6me peut ~tre faux si Singe) est de codimension 2; il ne semble pas admettre de b o n n e g6ndralisation au cas off r(co) < 1. 1, le feuilletage induit sur N(co) est minimal et uniquement ergodique. En particulier toute feuille de co est ferm6e (dans M*) ou localement dense, c'est ~t dire que co n'a pas de feuille exceptionhelle.

N o u s avons donc montr6 le th6or6me pour les formes de Morse. M. Dans le niveau f - l ( c ) c ~ M * qui contient L, il existe une composante L' (en fait unique) dont la projection L' rencontre C. Puisque L et E sont coup6es par des transversales ferm6es, Ies feuilIes L e t L' adh6rent ~t des composantes de M . . )~c, +6) sur lesquelles f n'est pas bornde. 1 que 5q(co) est strictement contenu dans Ker[co]; puisque codim S i n g e ) > 3, deux lacets de A~r* homotopes dans M ont le m6me h o m b r e d'intersection alg6brique avec L ou L'.

Math. Stud. 86 (1976) Princeton Univ. : Ergodicity of foliations with singularities. : On codimension one foliations defined by closed one forms with singularities. J. Math. Kyoto Univ. : Structure of codimension 1 foliations without holonomy on manifolds with abelian fundamental group. J. Math. Kyoto Univ. : Denjoy-Siegel theory of codimension one foliations. Sfigaku 32, 119-132 (1980) (en japonais). : Geometry and ergodicity of singular closed 1-forms. Proc. V Escola Geom. : On the volume elements on a manifold.

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1-formes ferm6es singuli6res et groupe fondamental by Levitt G.

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