On the topology of manifolds admitting diffeomorphisms with orientable expanding attractors and contracting repellers

In the talk we consider a class of diffeomorphisms defined on a closed orientable manifold of dimension $n>2$, whose nonwandering set consists of hyperbolic orientable basic sets of codimension one and arranges locally as the product of Cantor set and a disc of dimension $n-1$. It is established that the supporting manifold of a diffeomorphism from the class under consideration is homeomorphic to the connected sum of a finite number of manifolds homeomorphic to the torus and manifolds homeomorphic to the direct product of the sphere of dimension $n-1$ and the circle. The number of terms in a connected sum is determined by the number of basic sets and their properties.
The main result of the report was obtained in collaboration with E.V. Zhuzhoma and V.S. Medvedev.
The report was prepared with support of the Laboratory of Dynamical Systems and Applications NRU HSE, grant of the Ministry of science and higher education of the RF no. 075-15-2019-1931.