Handbook 1996 : Faculty of Science (Volume 4 page 213)
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618-322 Topology

Credit points: 15.0

Coordinator: Dr C Hodgson

Prerequisite: Mathematics 618-231, 618-301 and 321

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:

Comprehend:

• the basic concepts and examples of topological spaces;
• the definition of manifolds and the classification of surfaces;
• the idea of homotopy of mappings;
• how to calculate and use the fundamental group;
• the concept of covering spaces and their relationship with fundamental groups;
• the basic ideas of homology theory.

Have developed:

• skills in working with the fundamental group and homology groups;
• the ability to convert problems involving topological spaces and continuous maps into problems in algebra;
• the ability to distinguish between different topological spaces;
• the ability to construct homeomorphisms and homotopy equivalences between spaces.

Appreciate:

• the basic questions in topology;
• the power of topological methods in dealing with problems involving shape and position of objects and continuous mappings;
• how topology can be applied to many areas, including geometry, analysis, group theory and physics.

Content:

Introduction to topology: homotopy and the fundamental group of a space; covering spaces; simplicial homology. Introduction to manifolds: manifolds, tangent vectors, differential forms. Selection of additional topics: connections, Riemannian metrics, curvature, Gauss-Bonnet theorem; integration on manifolds, de Rham's theorem.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

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Handbook 1996 : Faculty of Science (Volume 4 page 213)

Status:          Official 1996
Date created:    Oct  9 1995
Last modified:   Oct  9 1995
Authorised by:   Academic Registrar
Email enquiries: Course_Information@registrar.unimelb.edu.au

Copyright © University of Melbourne 1995,1996.