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My research interests lie at the interface of algebraic and geometric topology. I like to take recent theories developed in algebaic topology, in particular the calculus of functors and equivariant stable homotopy theory, and apply them to answer concrete questions about manifolds, in particular about knots and group actions. The need to develop additional machinery has for example led to my interest in completions of configuration spaces, Lie coalgebras, and rational homotopy theory. You can learn more about various research threads by following the links to the right.

I post my preprints on the Mathematics ArXiv. This work is partially supported by the Division of Mathematical Sciences of the National Science Foundation.


Papers
PS PDF Operads and knot spaces.
Journal of the AMS, Vol 19 No 2 (2006) 461-486.
PS PDF New perspectives on self linking (with R. Budney, K. Scannell, and J. Conant) Advances in Mathematics, Vol 191 No 1 (2005), 78-113.
PS PDF Bordism of semi-free S1-actions.
Mathematische Zeitschrift, Vol 249 No 2 (2005) 439-454.
PS PDF Manifold-theoretic compactifications of configuration spaces.
Selecta Mathematica (new series) Vol 10, No 3 (2004) 391-428.
PS PDF A one-dimensional embedding complex. (with Kevin Scannell)
Journal of Pure and Applied Algebra 170 (2002) 93-107
PS PDF Computations of complex equivariant bordism rings.
American Journal of Mathematics 123 (2001) 577-605.
PS PDF Real equivariant bordism and stable transversality obstructions for G=Z/2
Proceedings of the AMS 130 (2002), No. 1, 271--281.
PS PDF The geometry of the local cohomology filtration in equivariant bordism.
Homotopy, Homology and Applications, vol 3(2), (2001), pp 385-406.

Preprints
PS PDF Lie coalgebras and rational homotopy theory, I. (with Ben Walter)
Submitted.
PS PDF The homology of the little disks operad.
Submitted.
PS PDF A pairing between graphs and trees.
Submitted.
PS PDF The topology of spaces of knots.
Submitted.