![]() The project aims to study noncompact, complete, finite volume, bounded, nonpositively curved manifolds M. Specifically, the PI will study the topology of ends as obstructions to having nonpositively curved metrics. The proposed research also aims to find topological properties shared by large classes of nonpositively curved manifolds and topological obstructions to having a nonpositively curved metric. The question whether a space admits a nonpositively curved metric has become of great interest in different areas in topology. If a space is known to have a nonpositively curved metric, one can deduce a lot about it. One of the aims of the proposed research is to construct more nonpositively curved manifolds, especially with interesting properties that are not seen in hyperbolic or pinched negatively curved manifolds. Constructions of smooth, nonpositively curved manifolds are poorly understood in the sense that most examples known are of a very restrictive type, such as hyperbolic manifolds and pinched negatively curved manifolds, which do not illustrate more generic properties of nonpositively curved spaces. ![]() The field, however, seems to have been abandoned in the last two decades although there are a lot of unanswered questions, some of which are within reach. Nonpositively curved manifolds (spaces) has been a subject where there are a lot of rich theorems, and it has been a central object of study not only in geometry, but also in related fields of mathematics, such as geometric group theory and dynamics. Primary Place of Performance Congressional District:Ī fundamental question of Geometry and Topology is how the global topology of a space is determined by local geometric data, in particular, the curvature of the space. Tu Tam Nguyen Phan (Principal Investigator) Sponsored Research Office:. ![]() Joanna Kania-Bartoszynska (703)292-4881 DMS Division Of Mathematical Sciences MPS Direct For Mathematical & Physical Scien RESEARCH FOUNDATION FOR THE STATE UNIVERSITY OF NEW YORK, THE Topology of non-positively curved manifolds NSF Org:
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