Conley index theory without index pairs

Date
2021/11/05 Fri 15:00 - 17:00
Speaker
Yosuke Morita
Affiliation
Kyoto University
Abstract

In this talk, we propose a new framework for Conley index theory of topological dynamical systems. In the traditional formulation, one uses an index pair (N, L) to construct the Conley index of isolated invariant subsets. However, in fact, N and L themselves are not important; one only needs the information on the difference set of N and L to develop Conley index theory. In our new formulation, we use the notions of compactifiable subsets and index neighbourhoods instead of index pairs.