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Title page for ETD etd-03272008-222931

Type of Document Dissertation
Author Nowak, Piotr Wojciech
URN etd-03272008-222931
Title Property A as metric amenability and its applications to geometry
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Guoliang Yu Committee Chair
Bruce Hughes Committee Member
Gennadi Kasparov Committee Member
Mark Sapir Committee Member
Thomas Kephart Committee Member
  • isoperimetric profile
  • asymptotic dimension
  • coarse embedding
  • Property A
Date of Defense 2008-03-21
Availability unrestricted
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.

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