[Binghamton Geometry/Topology Seminar] Geometry & Topology Seminar

[somnath at math.binghamton.edu]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

*Date:*  Thursday, February 20th, 2013

*Time:*  2:50-3:50pm
*Place:*  Library North 2205 followed by coffee/tea in the Anderson
Reading Room.

*Speaker: ** *Barry Minemyer (Alfred University)
*Title: * Intrinsic Isometric Embeddings of Pro-Euclidean Spaces.

*Abstract:*   In his book ``Partial Differential Relations", Gromov gives
the definition for an intrinsic isometry between metric spaces as a
generalization of the definition of an isometry between Riemannian
manifolds. In 2010, Petrunin proved that a compact metric space admits an
intrinsic isometry into n-dimensional Euclidean space if and only if it is
a pro-Euclidean space of rank at most n, and that either of these
assumptions implies that the Lebesgue covering dimension of X is at most
n. He also shows that this is not true, in general, for path isometries,
thus motivating the definition of an intrinsic isometry. One of the main
results of my thesis allows for a partial generalization of Petrunin's
result to intrinsic isometric embeddings. In this talk we will define all
of the necessary terminology, and sketch proofs of the various results.