A paradigm for codimension one foliations

Dmitry Filimonov (1) , Victor A. Kleptsyn (2) , Andrés Navas (3) , Bertrand Deroin (4)

1 HSE - Vysšaja škola èkonomiki = National Research University Higher School of Economics [Moscow]
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 USACH - Universidad de Santiago de Chile [Santiago]
4 DMA - Département de Mathématiques et Applications - ENS Paris

We summarize some of the recent works, devoted to the study of one-dimensional (pseudo)group actions and codimension one foliations. We state a conjectural alternative for such actions (generalizing the already obtained results) and describe the properties in both alternative cases. We also discuss the generalizations for holomorphic one-dimensional actions. Finally, we state some open questions that seem to be already within the reach.

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

Dmitry Filimonov, Victor A. Kleptsyn, Andrés Navas, Bertrand Deroin. A paradigm for codimension one foliations. Taro Asuke; Shigenori Matsumoto; Yoshihiko Mitsumatsu. Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, 72, Mathematical Society of Japan, Tokyo, pp.59-69, 2017, Advanced Studies in Pure Mathematics, 978-4-86497-040-2. ⟨hal-01654925⟩