4P3: Differential Topology (539.433)

The availability of units in Semester 1, 2, full year, etc. was correct at the time of going to press but may be subject to change. For the most up-to-date information click on the Timetable link below.

Credit: 6 points  Availability: Semester 1 (See Timetable)

Generally speaking, differential topology studies properties of smooth manifolds (i.e. smooth curves, surfaces and their higher-dimensional analogues) that are preserved under smooth deformations. This is naturally related to the study of certain features of smooth maps between manifolds. The unit covers the following main topics: smooth manifolds, regular points and regular values of smooth maps, immersions and submersions, Sard's Theorem, transversality, manifolds with boundary, smooth homotopy, degree of a smooth map, winding numbers and the Jordan-Brouwer Separation Theorem, index of a smooth vector field, the Poincare-Hopf Theorem, elements of dynamical systems - diffeomorphisms and flows, periodic points and orbits, Poincare maps, hyperbolicity, stable and unstable manifolds.

Unit Co-ordinator(s): Associate Professor Luchezar Stoyanov

Location: UWA (Crawley)

Mode: on-campus

Unit Rules:

Prerequisites: 2C1 and 2LA [From 2006: Calculus and Probability 209 (530.209) and Algebra 213 (530.213)]

Books and other material wherever listed may be subject to change. Book lists relating to 'Preliminary Reading', 'Recommended Reading' and 'Textbooks' are, in most cases, available at the University Co-operative Bookshop (from early January) and appropriate administrative offices for students to consult. For first-year units the Bookshop will endeavour to make available photocopies of book lists for individual units. Books marked with an asterisk (*) are available in paperback.