= John Milnor
{c}
<John Milnor> works across <topology>, <geometry> and <dynamical systems>. His expositions connect local calculations with global structure: <Morse Theory by John Milnor> develops the topology of a manifold through critical points, while his complex-dynamics lectures study iteration of holomorphic maps.<Morse Theory by John Milnor>[Lemma 2.2 and subsequent Morse-theoretic development]{ref}<Dynamics in one complex variable: introductory lectures by John Milnor>[Sections 2–3 and 7]{ref}
Near a nondegenerate critical point, the <Morse lemma> reduces a smooth function exactly to a signed quadratic form in suitable coordinates. Its index controls the topological change in sublevel sets. With <James D. Stasheff>, Milnor also wrote <Characteristic Classes by John Milnor and James D. Stasheff>, developing invariants of <vector bundles>.
Back to article page
