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Graduate Geometry and Topology Learning Seminar

Various constructions of the Poincare homology sphere

Sriram Raghunath - Rutgers University

Location:  Hill 701 (Graduate Student Lounge)
Date & time: Tuesday, 22 February 2022 at 5:15PM - 6:30PM

 Abstract : We have all heard about the Poincare conjecture – every compact simply connected 3-manifold without boundary is homeomorphic to the 3-sphere. But Poincare initially thought that any 3-manifold which has all its homology groups isomorphic to those of S3 should be homeomorphic to S3. This turned out to be spectacularly wrong – there are in fact infinitely many counterexamples to this statement. In fact, Poincare himself came up with the most famous counterexample of all – the Poincare homology sphere. In this talk, we will discuss multiple constructions of this space from different points of view – this is an excuse for me to talk about interesting techniques in low dimensional topology.

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