Speaker: Doron Shaharabani, TAU

Title: The Offset Filtration of Convex Objects in 3-Space

Abstract:
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We consider offsets of a union of convex objects. We aim
for a filtration, a sequence of nested cell complexes, that
captures the topological evolution of the offsets for
increasing radii. In this talk I will describe an efficient
construction of a filtered cell complex that carries the
same hole structure as offsets of convex of polyhedra in
R^3. As part of it, I will also prove that the Minkowski
sums of two disjoint convex polyhedra with a ball are
pseudo-spheres, namely, the intersection of their
boundaries is either empty, a single point, or homeomorphic
to a closed cycle.

This is joint work with Dan Halperin and Michael Kerber