Séminaire QUID

Quid of homology spheres?

by Adrien Rodau

Room Picard (1R2-129)

Room Picard (1R2-129)


The early history of topology began with the ideas of E. Betti and B. Riemann and the work of H. Poincaré on the concept of homology, quickly refined into the concept of homotopy. The infamous Poincaré conjecture (now theorem) states that no compact object has the same homotopy groups as the 3-sphere. But Poincaré originally believed the same about homology. This other conjecture was disproved by Poincaré himself by building a "homology sphere", a 3-dimensional object not homeomorphic to the 3-sphere but with the same homology groups. In this talk we present another method of building this homology sphere due to M. Dehn. This construction makes use of elementary tools from knot theory, homotopy and of course homology, which we present along the way.