Title:Fundamental Group and First Homology Group

Time: Thurs. Apr.13, 2017, PM 16:00-17:00

Speaker: Prof.Gregory R. Conner ( Brigham Young University )

Location:Room 4131, Building No.4, Wushan Campus

Abstract: One would often like to be able to check if two topological spaces are equivalent (homeomorphic).  Historically people have used invariants such as the fundamental group and homology to tell apart nice locally simple spaces such as manifolds and simplicial complexes.  Recently many questions have arisen in modern mathematics concerning spaces which are locally complicated such as attractors and boundaries.  We discuss how, in low dimensions, that homology is very poor at distinguishing between locally complicated spaces while the fundamental group is often a perfect invariant by discussing an interesting menagerie of examples.