3,176 research outputs found
Grothendieck–Verdier duality patterns in quantum algebra
After a brief survey of the basic definitions of the Grothendieck--Verdier
categories and dualities, I consider in this context introduced earlier
dualities in the categories of quadratic algebras and operads, largely
motivated by the theory of quantum groups. Finally, I argue that Dubrovin's
"almost duality" in the theory of Frobenius manifolds and quantum cohomology
also must fit a (possibly extended) version of Grothendieck--Verdier duality.Comment: 13 pages, accepted for publication in Izvestiya: Mathematic
BU Libraries self-care "Take a coloring break" posters
These posters were created to encourage self-care and healthy habits during exam periods at BU
Volume distortion in homotopy groups
Given a finite metric CW complex and an element ,
what are the properties of a geometrically optimal representative of ?
We study the optimal volume of as a function of . Asymptotically,
this function, whose inverse, for reasons of tradition, we call the volume
distortion, turns out to be an invariant with respect to the rational homotopy
of . We provide a number of examples and techniques for studying this
invariant, with a special focus on spaces with few rational homotopy groups.
Our main theorem characterizes those in which all non-torsion homotopy
classes are undistorted, that is, their distortion functions are linear.Comment: 49 pages, 4 figures. Accepted for publication in Geometric and
Functional Analysis (GAFA
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