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MA3F1 Introduction to Topology

Lecturer: Colin Sparrow

Term(s): Term 1

Status for Mathematics students: List A

Commitment: 30 one-hour lectures (or equivalent in 20/21)

Assessment: One 3-hour examination (85%), assignments (15%)

Prerequisites: MA132 Foundations, MA251 Algebra I, MA260 Norms, Metrics and Topologies (or MA222 Metric Spaces).

Leads To: MA3H6 Algebraic Topology, MA3H5 Manifolds, MA4J7 Cohomology and Poincaré Duality.

Topology is the study of properties of spaces invariant under continuous deformation. For this reason it is often called "rubber-sheet geometry''. The module covers: topological spaces and basic examples; compactness; connectedness and path-connectedness; identification topology; Cartesian products; homotopy and the fundamental group; winding numbers and applications; an outline of the classification of surfaces.

To introduce and illustrate the main ideas and problems of topology.

To explain how to distinguish spaces by means of simple topological invariants (compactness, connectedness and the fundamental group). To explain how to construct spaces by gluing and to prove that in certain cases that the result is homeomorphic to a standard space; to construct simple examples of spaces with given properties (e.g. compact but not connected or connected but not path connected).

Chapter 1 of Allen Hatcher's book Algebraic Topology

For more reading, see the Moodle Pages (link below). MA Armstrong Basic Topology Springer (recommended but not essential).

Additional Resources (Moodle pages)

Archived Pages: 2011 2012 2013 2014 2015 2016 2017