Realising sets of integers as mapping degree sets
Christoforos Neofytidis, Shicheng Wang, Zhongzi Wang
Source abstract
Abstract Given two closed oriented manifolds of the same dimension, we denote the set of degrees of maps from to by . The set always contains zero. We show the following (non‐)realisability results. There exists an infinite subset of containing 0 which cannot be realised as , for any closed oriented ‐manifolds . Every finite arithmetic progression of integers containing 0 can be realised as , for some closed oriented 3‐manifolds . Together with 0, every finite geometric progression of positive integers starting from 1 can be realised as , for some closed oriented manifolds .
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