dc.creator | Nowak, Piotr Wojciech | |
dc.date.accessioned | 2020-08-22T00:05:11Z | |
dc.date.available | 2010-04-25 | |
dc.date.issued | 2008-04-25 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-03272008-222931 | |
dc.identifier.uri | http://hdl.handle.net/1803/11496 | |
dc.description.abstract | Property 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.format.mimetype | application/pdf | |
dc.subject | isoperimetric profile | |
dc.subject | asymptotic dimension | |
dc.subject | coarse embedding | |
dc.subject | Property A | |
dc.title | Property A as metric amenability and its applications to geometry | |
dc.type | dissertation | |
dc.contributor.committeeMember | Thomas Kephart | |
dc.contributor.committeeMember | Gennadi Kasparov | |
dc.contributor.committeeMember | Mark Sapir | |
dc.contributor.committeeMember | Bruce Hughes | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2010-04-25 | |
local.embargo.lift | 2010-04-25 | |
dc.contributor.committeeChair | Guoliang Yu | |