Mathematics Colloquia and Seminars

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It is a foundational result in low-dimensional topology that every 2-manifold has a triangulation. The same is true for 3-manifolds, a result without which modern 3-manifold topology would not exist. However, there exist high-dimensional manifolds without triangulations. In this talk we will see some common techniques in proving triangulability, including an introduction to piecewise linear manifolds. We will also see an outline of why 2-manifolds are triangulable as well as an indication of why triangulability can fail for high-dimensional manifolds.