Research

Interests

I work on problems in smooth 4-manifolds. I find low-dimensional topology (which includes dimension 4) very hands-on because I can construct the objects that I'm interested in directly. In the case of 4-manifolds, this can be done through the use of ``handlebody theory.'' My recent projects involve answering questions about 4-manifolds using handle theory coupled with techniques drawn from symplectic and contact geometry as well as gauge theory.

Research Statement

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Preprints

  • On Handlebody Structures of Rational Balls, arXiv e-prints (2014), 1406.1575.
  • Obstructing Sliceness in a Family of Montesinos Knots, arXiv e-prints (2008), 0809.1247.

Resources

Selman Akbulut's 4-Manifolds Book Project » MathSciNet » arXiv.org » Math Overflow » MSU's e-Resources for Mathematics » $\TeX$ Users Group » $\LaTeX$ Symbols » Inkscape »