Teaching:

Research:

I study 3-dimensional topology, especially knots, links, and hyperbolic 3-manifolds. My advisor was Alan Reid at the University of Texas.

Papers, Preprints, and Slides:

• Some Virtually Special Hyperbolic 3-Manifold Groups (with Jason Deblois and Henry Wilton). Preprint.

  We show that hyperbolic 3-manifolds that admit a decomposition into right-angled ideal polyhedra are virtually fibered and LERF.  The paper includes numerous examples.

• Trace Fields and commensurability of link complements (with Jason Deblois). Submitted.

  We construct an infinite family of hyperbolic two-component links whose complements share a trace field but are incommensurable.  Related constructions give infinitely many two-component links with non-integral traces  and infinitely manycommensurability classes of one-cusped manifolds sharing a trace field.

• Not all boundary slopes are strongly detected by the character variety (with Stephan Tillmann). Communications in Analysis and Geometry Vol. 15 (2007), no. 4.

  We answer the question of whether all boundary slopes of a hyperbolic 3-manifold are strongly detected by the character variety by giving an infinite family of hyperbolic links which have boundary slopes that are not strongly detected.

• All roots of unity are detected by the A-polynomial. Algebraic & Geometric Topology, Vol. 5 (2005) 207-217.

  I answer a question of Cooper, Culler, Gillet, Long, and Shalen as to which roots of unity can arise when a boundary slope is strongly detected by the character variety.  For each positive integer n, I give examples of infinitely many hyperbolic manifolds where every nth root of unity arises in this process.

• Undetected boundary slopes and roots of unity for the character variety of a 3-manifold. 

  Thesis.

• Special links. Slides for a talk at the La-Tx Topology Retreat, Feb. 10, 2008.

Sculpture:

Other:

My wife, Kelly McKinnie, is also an instructor at  the U of M. She studies algebra.

Here are some more pictures.