Quantitative Topology III
16:00 - 17:30
In Lecture 2, we described how (Guth's version of) the method of CDMW gives an affirmative answer to the question "Given a null-homotopic map f from S^m to S^n with Lipschitz constant L, is there a null homotopy of f with Lipschitz constant < C(m,n).L?" for the case when the dimension of the target sphere S^n is odd.
In Lecture 3, we will discuss how this method gives an affirmative answer for the more general case when the target sphere S^n is replaced by a complex X that is rationally a product of Eilenberg-MacLane spaces.
If time permits, we will give a (counter)example of a complex Y and a null homotopic map g from S^m to Y that has Lipschitz constant L but any null homotopy of g has Lipschitz constant of the order L^r, for some r >1.