Li Chen, Department of Pure Mathematics, University of Waterloo
“No Morse, this is it!”
We will prove ”Morse Theorem”, so-to-speak, in this talk modulo some technical details. So far we have seen the basic ideas and some examples from Morse theory. I’d like to show that, under suitably nice assumptions, the index of a smooth function, f, at a non-degenerate critical point, p, provide us a way to attach a cell to Mc−ε such that the resulting object is homotopy equivalent to Mc+ε where f(p) = candMa = f−1((−∞,a]).