On PM-mapping class monoids

TL;DR

This paper introduces PM-mapping class monoids, drawing analogies with braid groups and inverse mapping class monoids, and proves an analog of the Dehn-Nielsen-Baer theorem to deepen understanding of their structure.

Contribution

It defines PM-mapping class monoids and establishes an analog of the Dehn-Nielsen-Baer theorem, extending the theory of mapping class groups.

Findings

Introduction of PM-mapping class monoids

Establishment of an analog of the Dehn-Nielsen-Baer theorem

Extension of the theory of mapping class groups

Abstract

In this paper, we introduce PM-mapping class monoids. Braid groups and mapping class groups have many features in common. Similarly to the notion of braid PM-monoid, PM-mapping class monoid is defined. This construction is an analogy of inverse mapping class monoid defined by R. Karoui and V. V. Vershinin. As the main result, we give the analog of the Dehn-Nilsen-Baer theorem.