21,724 research outputs found
Donaldson-Thomas theory and cluster algebras
We provide a transformation formula of non-commutative Donaldson-Thomas
invariants under a composition of mutations. Consequently, we get a description
of a composition of cluster transformations in terms of quiver Grassmannians.
As an application, we give an alternative proof of Fomin-Zelevinsky's
conjectures on -polynomials and -vectors.Comment: 39 pages, 8 figures, mostly rewritte
On continuous extension of grafting maps
The definition of the grafting operation for quasifuchsian groups is extended
by Bromberg to all -groups. Although the grafting maps are not necessarily
continuous at boundary groups, in this paper, we show that the grafting maps
take every "standard" convergent sequence to a convergent sequence. As a
consequence of this result, we extend Goldman's grafting theorem for
quasifuchsian groups to all boundary -groups.Comment: 24 pages, 2 figure
Criteria for D_4 singularities of wave fronts
We give useful and simple criteria for determining D_4 singularities of wave
fronts. As an application, we investigate behaviors of singular curvatures of
cuspidal edges near D_4^+ singularities.Comment: 11 pages with 4 figure
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