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Equivariant infinite dimensional topology


The main objective of this proposal is to continue the study of actions of groups on Q-manifolds and in particular to study the topology of orbit spaces of such actions. The examples of the main interests will be actions of compact groups on hyperspaces of Peano continua induced by actions of those groups on the continua. I plan to extend my results concerning Q-manifold structure of such quotient spaces and of Banach-Mazur compacta.

I will also study in details such Q-manifolds structures trying to get the explicit forms of them, as a question of its own interest and as a tool for investigating further properties, in particular for describing the homotopy type of such orbit spaces. All those questions will lead to systematic treatment of the problem of actions of compact groups on Q-manifolds. I will be mainly working with Prof. Cauty, leading specialist in the area of infinite-dimensional topology. Some of the interests of Prof. Cauty (the questions of actions of finite groups on ANR) are directly related to the objectives of this proposal (concerning actions of finite groups on the Hilbert cube).

Therefore I believe that the results obtained by me up to now and their planned extension will be of great interest to the topology group of Prof. Cauty. The training through research and through interactions in Paris will leave me excellently placed for a permanent academic position and will develop a solid base for further cooperation in research.

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