# MA3F1 Introduction to Topology

**Lecturer: **Saul Schleimer

**Term(s):** Term 1

**Status for Mathematics students:** List A

**Commitment:** 30 one-hour lectures

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

**Prerequisites:** MA129 Foundations, MA242 Algebra I, MA222 Metric Spaces

**Leads To: **MA408 Algebraic Topology,MA455 Manifolds, MA3F2 Knot Theory.

**Content**:

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.

**Aims**:

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

**Objectives**:

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 (eg compact but not connected or connected but not path connected).

**Books**:

Chapter 1 of Allen Hatcher's book Algebraic Topology

MA Armstrong *Basic Topology* Springer (recommended but not essential).