Algebraic Topology: Algebraic Invariants of Spaces - Oxford Mathematics 4th Year Lecture

This is the first hour of André Henriques' fourth year Algebraic Topology course (a second lecture will follow soon). We recall a known algebraic invariants of spaces, the fundamental group, and spell out its desired properties (homotopy invariance). We then hint at some other algebraic invariants with similar properties, such as higher homotopy groups, homology, and cohomology. You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE All first and second year lectures are followed by tutorials where students meet their tutor in pairs to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.