Mednykh, Alexander; Matematični kolokvij april 2011

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Counting coverings and maps

Alexander Mednykh

Sobolev Institute of Mathematics,
Novosibirsk State University, Rusija

21. april 2011


In this lecture we give a new method to count finite sheeted coverings of manifolds with a finitely generated fundamental group. We apply it to count branched and unbranched coverings over compact surfaces (bordered or with empty border).

As a consequence, we suggest a new approach to count maps on surfaces up to orientation preserving homeomorphism. The further development of the method gives us a possibility to count chiral maps (or twins) by number of edges on a closed orientable surface.


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