Welcome to Geometry & Topology

The Geometry & Topology research group at the University of Waterloo is a young and very active group. We have frequent seminars, specialized graduate courses, visitors, and postdoctoral fellows. If you are interested in graduate studies or postdoctoral fellowship opportunities in geometry and topology at Waterloo, please contact one of the group's faculty members.

Some of the research interests of our group include

  • low dimensional topology
  • gauge theory
  • symplectic and complex geometry
  • arithmetic geometry
  • special holonomy and calibrations
  • applications of geometry to physics
  • toric geometry

Geometry and Topology seminars


Thursday, February 2, 2023 2:30 pm - 3:30 pm EST

Spin^h and further generalisations of spin

Michael Albanese, Department of Pure Mathematics, University of Waterloo

The question of which manifolds are spin or spin^c has a simple and complete answer. In this talk we address the same question for the lesser known spin^h manifolds which have appeared in geometry and physics in recent decades. We determine the first obstruction to being spin^h and use this to provide an example of an orientable manifold which is not spin^h. The existence of such an example leads us to consider an infinite sequence of generalised spin structures. In doing so, we determine an answer to the following question: is there an integer k such that every manifold embeds in a spin manifold with codimension at most k?

This is joint work with Aleksandar Milivojevic.

MC 5417