Realising sets of integers as mapping degree sets

Autor:	Neofytidis, Christoforos, Wang, Shicheng, Wang, Zhongzi
Rok vydání:	2021
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Topology Mathematics - Number Theory
Zdroj:	Bull. Lond. Math. Soc. 55 (2023), 1700--1717
Druh dokumentu:	Working Paper
Popis:	Given two closed oriented manifolds $M,N$ of the same dimension, we denote the set of degrees of maps from $M$ to $N$ by $D(M,N)$. The set $D(M,N)$ always contains zero. We show the following (non-)realisability results: (i) There exists an infinite subset $A$ of $\mathbb Z$ containing $0$ which cannot be realised as $D(M,N)$, for any closed oriented $n$-manifolds $M,N$. (ii) Every finite arithmetic progression of integers containing $0$ can be realised as $D(M,N)$, for some closed oriented $3$-manifolds $M,N$. (iii) Together with $0$, every finite geometric progression of positive integers starting from $1$ can be realised as $D(M,N)$, for some closed oriented manifolds $M,N$. Comment: 17 pages; v2: final version, to appear in Bulletin of the London Mathematical Society
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.13790 Zobrazit plný text záznamu View this record from Arxiv