图形之间的多重松散映射

IF 0.6 4区数学 Q3 MATHEMATICS Bulletin of the Australian Mathematical Society Pub Date : 2024-04-22 DOI:10.1017/s0004972724000297

MARCIO COLOMBO FENILLE

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引用次数: 0

摘要

给定（有限连通）图之间的映射 $f_1,\ldots ,f_n:X\to Y$，且 $n\geq 3$（众所周知的情况是 $n=2$），如果它们可以通过同调变形为无重合映射，我们就说它们是松散的；如果它们可以通过同调变形为二乘二无重合映射，我们就说它们是完全松散的。我们证明(i) 如果 Y 与圆不同构，那么任何映射都是完全松散的；(ii) 否则，任何映射都是松散的，而且只有当它们是同构的时候，它们才是完全松散的。

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MULTIPLE LOOSE MAPS BETWEEN GRAPHS

Given maps

$f_1,\ldots ,f_n:X\to Y$

between (finite and connected) graphs, with

$n\geq 3$

(the case

$n=2$

is well known), we say that they are loose if they can be deformed by homotopy to coincidence free maps, and totally loose if they can be deformed by homotopy to maps which are two by two coincidence free. We prove that: (i) if Y is not homeomorphic to the circle, then any maps are totally loose; (ii) otherwise, any maps are loose and they are totally loose if and only if they are homotopic.

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society

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