This dissertation establishes three coarse geometric analogues of algebraic coherence: geometric coherence, coarse coherence, and relative coarse coherence. Each of these coarse geometric coherence notions is a coarse geometric invariant. Several permanence properties of these coarse invariants are demonstrated, elementary examples are computed, and the relationships that these properties have with one another and with other previously established coarse geometric invariants are investigated. Significant results include that the straight finite decomposition complexity of A. Dranishnikov and M. Zarichnyi implies coarse coherence, and that M. Gromov's finite asymptotic dimension implies coherence, coarse coherence, and relative coarse coherence. Further, as a consequence of a theorem of D. Kasprowski, A. Nicas, and D. Rosenthal, the collection of countable groups with coarse coherence is closed under extensions and free products, and includes all elementary amenable, all linear, and subgroups of virtually connected Lie groups.
|Commitee:||Srivastav, Anupam, Tchernev, Alexandre, Varisco, Marco|
|School:||State University of New York at Albany|
|Department:||Mathematics and Statistics|
|School Location:||United States -- New York|
|Source:||DAI-B 80/09(E), Dissertation Abstracts International|
|Keywords:||Coarse, Coherence, Geometry, Mathematics, Metric, Topology|
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