Research Interests

(Technical version)

My research area is geometric topology¾primarily the topology of manifolds. Manifold topology is frequently broken into the following sub-areas: low dimensional (2- and 3-manifolds), 4-dimensional (an area unto itself), high dimensional (finite dimensions >4), and infinite dimensional topology. I have done a little work in low dimensions, and a little more in dimension 4 (including my Ph.D. thesis). I maintain a strong interest in 4-manifold topology, and hope to get back to some problems in that area soon. Infinite dimensional (Hilbert cube) manifolds play a role in some of my recent work. However, the largest part of my research has involved high dimensional manifolds.

In recent years I have been particularly interested in non-compact manifolds and complexes. Current work in geometric group theory¾ along with new approaches to the Borel and Novikov Conjectures in manifold topology¾suggest that an expanded theory of non-compact spaces is needed. I am especially interested in Z-compactifications of open manifolds and complexes, and structure theorems for open manifolds with non-stable fundamental groups at infinity. Of special interest are universal covers of aspherical manifolds, and manifolds which admit CAT(0) metrics (a generalized version of non-positive curvature).

You can learn more about my research by browsing my publication list or by downloading a preprint. If you are interested in a paper that is not posted, Id be happy to send you a hard copy. If you are a student interested in studying topology, be sure to click here.

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CRAIG R. GUILBAULT Professor, Mathematical Sciences  University of Wisconsin- Milwaukee