Department of Mathematics

Topology


Topology is the field of Mathematics that studies properties of spaces and objects which are not affected by continuous deformations. For instance, properties such as length or curvature are not topological while the number of holes in an object is a topological property. Topology has tight connections and many interactions with other fields, including Differential Geometry, Algebra, Combinatorics, Mathematical Physics and Applied Mathematics. The research interests of our Topology faculty are very diverse and cover several topics such as:

  • 4-manifold topology and gauge theory.
  • Symplectic and contact topology.
  • Topology of manifolds with special holonomy.
  • 3-manifold topology and geometry.
  • Quantum topology and Knot theory.
  • Geometric Group Theory.
  • Algebraic Topology and K-Theory.
  • Topology of real algebraic sets.
  • Applied topology.

Our group works closely with the Differential Geometry and Geometric Analysis group. We have many overlapping interests and hold many joint seminars. In particular, the combined Geometry & Topology group at MSU has a long history in mentoring and training successful graduate students and postdoctoral fellows.