Homotopy properties of smooth functions on surfaces

Iryna Kuznietsova
Institute of Mathematics of the National Academy of Sciences of Ukraine

Date(s) : 24/11/2022   iCal
11 h 00 min - 12 h 00 min


Let $M$ be a smooth compact surface. Consider the natural action of the group $D(M)$ of diffeomorphisms on the space of smooth functions $С^\infty(M,R)$ such that the result of the action of the diffeomorphism $h$ on the function $f$ is the composition $f\circ h$.

I will talk about homotopy types of orbits and stabilizers of Morse functions under this action.

In particular, if $M$ has negative Euler characteristic, then computation of such homotopy types reduces to the computation of fundamental groups of orbits of functions only on cylinders, disks and Möbius bands. These groups for disks and cylinders were computed by Sergyi Maksymenko and appeared to be generated by direct and some sorts of wreath products. This talk will focus on the current progress for the case of Möbius band and is based on a joint work with Sergyi Maksymenko.

FRUMAM, St Charles


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