The Hilbert cube is a product of a countable number of closed intervals endowed with the Tikhonov topology. Although this is an infinite-dimensional object, it turns out to be useful for proving statements about finite simplicial complexes. Namely, in the early 1970s, T.Chapman used it to prove the topological invariance of the Whitehead torsion, a special case of which, the Reidemeister torsion, is actively used to this day in low-dimensional topology.

The course will present classical results on the Hilbert cube, including the proof of Chapman's result mentioned above, and discuss what implications they have for low-dimensional topology.

The course assumes that students are familiar with the elements of algebraic and homotopy topology: the concepts of CW-complex, manifold, homology.

Please, address Ivan Dynnikov, dynnikov@mech.math.msu.su, for Zoom data.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2022-265).

Lecturers
Dynnikov Ivan Alekseevich
Prasolov Maxim Vyacheslavovich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center