Title: Characterizations of coarse and uniform embeddability into c_0(k)
By: Dr. Andrew Swift, Oklahoma University
Abstract: Nonlinear geometry of Banach spaces has found applications in computer science and research into famous mathematical conjectures such as the Novikov conjecture. One of the major open questions in the field is whether the coarse (large-scale) embeddability of a Banach space into another is equivalent to the uniform (small-scale) embeddability. I will give a brief introduction to both types of embeddability and show that if the target space is c_0(k), where k is any cardinality, then the two types of embeddability are equivalent. Both types of embeddability in this case can be characterized intrinsically in terms of metric covers using properties (uniform/coarse Stone property) analogous to the notion of paracompactness from topology. These properties may be viewed as generalizations of the property that a space has finite (Lebesgue covering/asymptotic) dimension.
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