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Working paper

Basic automorphism groups of complete Cartan foliations covered by fibrations

arxiv.org. math. Cornell University, 2015. No. 1410.1144 .
Zhukova N.I., K. I. Sheina.
We get sufficient conditions for the full basic automorphism group of a complete Cartan foliation to admit a unique (finite-dimensional) Lie group structure in the category of Cartan foliations. In particular, we obtain sufficient conditions for this group to be discrete. Emphasize that the transverse Cartan geometry may be noneffective. Some estimates of the dimension of this group depending on the transverse geometry are found. Further, we investigate Cartan foliations covered by fibrations and ascertain their specification. Examples of computing the full basic automorphism group of complete Cartan foliations are constructed.