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Flattening A Cone, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

We want to manufacture a cut-off slanted cone from a flat sheet of metal. If the cone were a normal right cone we know that we would simply cut out a sector of a circle and roll it up. However the cone is slanted. We want to know what the flattened shape looks like so that we can cut it out and roll it up to closely approximate correct final shape. We also want to minimize the amount of wasted metal after the shape is cut out.

The problem, and it generalizations may be solved analytically but the analytical solution …

Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au

Department of Mathematics: Dissertations, Theses, and Student Research

Mu-Wan Huang, Mark Walker and I established an explicit formula for the equivariant K-groups of affine toric varieties. We also recovered a result due to Vezzosi and Vistoli, which expresses the equivariant K-groups of a smooth toric variety in terms of the K-groups of its maximal open affine toric subvarieties. This dissertation investigates the situation when the toric variety X is neither affine nor smooth. In many cases, we compute the Čech cohomology groups of the presheaf K_q^T on X endowed with a topology. Using these calculations and Walker's Localization Theorem for equivariant K-theory, we give explicit formulas …