Algebra Seminar: Robert Gray -- One-relator groups, monoids and inverse monoids

Robert Gray is speaking in the Algebra Seminar this week.  We will go out for lunch
after the talk.  

When: Friday 12 May, 12-1pm 

Where: Carslaw 173 

Title: One-relator groups, monoids and inverse monoids 

Abstract: It is a classical result of Magnus proved in the 1930s that the word problem
is decidable for one-relator groups.  In contrast, it remains a longstanding open
problem whether the word problem is decidable for one-relator monoids.  A natural class
of algebraic structures lying between monoids and groups is that of inverse monoids.  An
inverse monoid is called special if it is defined by a presentation where all the
defining relations are of the form w=1.  There is strong motivation for studying this
class coming from results of Ivanov, Margolis and Meakin (2001) who showed that if all
special one-relator inverse monoids with defining relator w=1, where w is a reduced
word, have decidable word problem then this would answer positively the open problem of
whether all one-relator monoids have decidable word problem.  In this talk I will speak
about some recent results on the algebraic and algorithmic properties of special and
one-relator inverse monoids.  I will explain some of the methods used in this area
including the theory of Schutzenberger graphs.  I’ll also explain the connections with
some problems about one-relator groups including the submonoid membership problem,
coherence, and the question of which right-angled Artin groups embed as subgroups.