Modern Differential Geometry and Topology - MATH5700
Faculty: Faculty of Science
School: School of Mathematics and Statistics
Course Outline: http://www.maths.unsw.edu.au/
Campus: Sydney
Career: Postgraduate
Units of Credit: 6
EFTSL: 0.12500 (more info)
Indicative Contact Hours per Week: 4
CSS Contribution Charge: 2 (more info)
Tuition Fee: See Tuition Fee Schedule
Further Information: See Class Timetable
Description
Topology and differential geometry both deal with the study of shape: topology from a continuous and differential geometry from a differentiable viewpoint.
This course begins with an introduction to general topology. We then study curves in space and how they bend and twist, and the topology of curves. We then consider surfaces, studying the first and second fundamental forms introduced by Gauss, the various measures of curvature and what they mean for the external and internal appearance and properties of surfaces. We prove the important Gauss-Bonnet theorem and use it to examine topological properties of surfaces, such as the Euler Characteristic. We finish with a look at the hyperbolic plane and a look forward to general Riemannian geometry.
This course begins with an introduction to general topology. We then study curves in space and how they bend and twist, and the topology of curves. We then consider surfaces, studying the first and second fundamental forms introduced by Gauss, the various measures of curvature and what they mean for the external and internal appearance and properties of surfaces. We prove the important Gauss-Bonnet theorem and use it to examine topological properties of surfaces, such as the Euler Characteristic. We finish with a look at the hyperbolic plane and a look forward to general Riemannian geometry.