Postgraduate Course: AGQ Differential Topology (MATH11255)

Course Outline
School	School of Mathematics	College	College of Science and Engineering
Credit level (Normal year taken)	SCQF Level 11 (Postgraduate)	Availability	Not available to visiting students
SCQF Credits	15	ECTS Credits	7.5
Summary	This course covers several fundamental topics in Geometry & Topology, providing a solid and broad foundation to the subject and its interactions with algebra and analysis. The course discusses the vector bundles, connections, principal bundles, characteristic classes, etc.
Course description	The course will start with a refresher about manifolds, vector bundles and fiber bundles. It will then discuss in detail various aspects of calculus on manifolds, introducing the Lie derivative, the exterior derivative, connections, holonomy, curvature and the Stokes Theorem. This will be followed by an exposition of de Rham cohomology and its relation to Cech cohomology. Finally, the central part of the course is an introduction to Chern-Weil theory and characteristic classes. If time permits, and based on the interests of students, additional topics such as elliptic operators and Dirac operators may be touched. Unless otherwise noted, the details of the content of this course can be found on the Scottish Mathematical Sciences Training Centre web site www.smstc.ac.uk, and/or the CDT webpage http://www.agq-cdt.org

Entry Requirements (not applicable to Visiting Students)
Pre-requisites		Co-requisites
Prohibited Combinations		Other requirements	None

Course Delivery Information

Academic year 2024/25, Not available to visiting students (SS1)		Quota: None
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 150 ( Lecture Hours 20, Seminar/Tutorial Hours 10, Programme Level Learning and Teaching Hours 3, Directed Learning and Independent Learning Hours 117 )
Assessment (Further Info)	Written Exam 0 %, Coursework 100 %, Practical Exam 0 %
Additional Information (Assessment)	Coursework : 100%«br /» Examination : 0%
Feedback	Not entered
No Exam Information

Learning Outcomes
On completion of this course, the student will be able to: Thoroughly understand the applications of differential topology to the local and global geometry of manifolds. Solve problems involving characteristic classes, vector bundles, differential forms, etc. from first principles.