Show simple item record

Property A as metric amenability and its applications to geometry

dc.creatorNowak, Piotr Wojciech
dc.description.abstractProperty A was introduced by Guoliang Yu as a metric version of a well-known group invariant, amenability. The new notion turned out to be extremely useful in several areas of mathematics. We prove an averaging theorem for Property A and explore its applications. The first is a construction of metric spaces which do not have Property A but admit a coarse embedding into a Hilbert space. This gives an answer to an open problem in coarse geometry and disproves a conjecture due to A.N.Dranishnikov. The second is a connection between type of asymptotic dimension and isoperimetric profiles, which allows to answer an open question of J.Roe. The third application is a proof of the zero-in-the-spectrum conjecture on certain Galois covers of compact manifolds.
dc.subjectisoperimetric profile
dc.subjectasymptotic dimension
dc.subjectcoarse embedding
dc.subjectProperty A
dc.titleProperty A as metric amenability and its applications to geometry
dc.contributor.committeeMemberThomas Kephart
dc.contributor.committeeMemberGennadi Kasparov
dc.contributor.committeeMemberMark Sapir
dc.contributor.committeeMemberBruce Hughes
dc.type.materialtext University
dc.contributor.committeeChairGuoliang Yu

Files in this item


This item appears in the following Collection(s)

Show simple item record