Riemannian geometry of compact metric spaces

dc.contributor.advisor Bellissard, Jean
dc.contributor.author Palmer, Ian Christian en_US
dc.contributor.committeeMember Bakhtin, Yuri
dc.contributor.committeeMember Belegradek, Igor
dc.contributor.committeeMember Cvitanovic, Predrag
dc.contributor.committeeMember Gangbo, Wilfrid
dc.contributor.department Mathematics en_US
dc.date.accessioned 2010-09-15T18:54:43Z
dc.date.available 2010-09-15T18:54:43Z
dc.date.issued 2010-05-21 en_US
dc.description.abstract A construction is given for which the Hausdorff measure and dimension of an arbitrary abstract compact metric space (X, d) can be encoded in a spectral triple. By introducing the concept of resolving sequence of open covers, conditions are given under which the topology, metric, and Hausdorff measure can be recovered from a spectral triple dependent on such a sequence. The construction holds for arbitrary compact metric spaces, generalizing previous results for fractals, as well as the original setting of manifolds, and also holds when Hausdorff and box dimensions differ---in particular, it does not depend on any self-similarity or regularity conditions on the space. The only restriction on the space is that it have positive s₀ dimensional Hausdorff measure, where s₀ is the Hausdorff dimension of the space, assumed to be finite. Also, X does not need to be embedded in another space, such as Rⁿ. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/34744
dc.publisher Georgia Institute of Technology en_US
dc.subject Noncommutative Geometry en_US
dc.subject Metric Spaces en_US
dc.subject.lcsh Geometry, Riemannian
dc.subject.lcsh Metric spaces
dc.subject.lcsh Hausdorff measures
dc.title Riemannian geometry of compact metric spaces en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Bellissard, Jean
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isAdvisorOfPublication ba697900-ef37-4f7b-9e1e-c6fe69757c4d
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
555.92 KB
Adobe Portable Document Format