Realising sets of integers as mapping degree sets (Christoforos Neofytidis, Ohio State University)

21.06.2022 10:30

A long-standing topic in the study of manifolds is the computation of all possible degrees of maps between two given closed manifolds. To this end, significant tools have been developed, including coarse geometric methods (negative curvature and harmonic mappings), global analytic concepts (Gromov's simplicial volume), as well as algebraic techniques (fundamental group and cohomology structures). In this talk, we initiate the opposite direction, relating number theoretic notions to topological data: Which subsets of the integers are realisable as mapping degree sets? On the one hand, we explain that arbitrary infinite sets are quite often not realisable, and, on the other hand, we show how to realise large classes of finite sets, including all arithmetic and positive geometric progressions. Joint work with S. Wang (Peking University) and Z. Wang (Tsinghua University).

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Tuesday 21.06.2022, Att. unusual place, Séminaire "Groupes et géométrie"

entrée libre