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Algebra Seminar
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David Easdown
University of Sydney

Braids and factorizable inverse monoids

Friday 13th, December 12:05-12:55pm, Carslaw 373.

What is the untangling effect on a braid if one is allowed to snip a string, or if two specified strings are allowed to pass through each other, or even allowed to merge and part as newly reconstituted strings? To calculate the effects, one works in an appropriate factorizable inverse monoid, some aspects of a general theory which will be discussed. The coset monoid of a group arises, and turns out to have a universal property within a certain class of factorizable inverse monoids. This theory is dual to the classical construction of fundamental inverse semigroups from semilattices.