Metrics on doubles as an inverse semigroup

Abstract: Usually metrics do not form an algebraic structure. I was interested in various metrics on two copies (double) of a metric space $(X,d)$ such that the metric on each copy is $d$, and only distances between points on different copies of $X$ may vary. To my surprise, if one passes from metrics to their equivalence classes (either quasi-equivalence or coarse equivalence) then the metrics on the double of $X$ form an inverse semigroup. Inverse semigroups are similar to sets of partial isometries on a Hilbert space, and one may define a C*-algebra of an inverse semigroup along the same guidelines as group C*-algebras. I shall speak about some results on these inverse semigroups, e.g. when they are commutative, and when they have a kind of finiteness property, i.e. when the unit is Murray-von Neumann equivalent to a proper projection.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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