# Math 652: Topology 2

## Contents

## Catalog Information

### Title

Topology 2.

### Credit Hours

3

### Prerequisites

Math 553, 554, and either 651 or consent of the instructor.

### Description

Advanced topics in topology. Topics may include, but are not limited to, piecewise linear topology, 3-manifold theory, homotopy theory, differential topology, Riemannian geometry, and geometric group theory

## Desired Learning Outcomes

Math 651 and 652 present advanced topics in topology. Topics are picked according to the developing interests of the research community and may also be helpful for students studying algebraic geometry or dynamical systems. Topics may include, but are not limited to, the topology of low-dimensional manifolds, piecewise linear topology, geometric group theory, and homotopy theory. For research preparation, the student should also consider courses in algebraic topology, differential topology, and Riemannian geometry.

Students should learn the foundational theorems in their fields of interest. Students should learn to find and read research papers in those fields. Students should learn to solve challenging problems, develop proofs of theorems on their own, and present those proofs clearly and coherently with appropriate illustrative examples.

### Minimal Learning Outcomes

We view Math 651 and 652 are an integrated 2-course series, with a certain amount of flexibility built in to accommodate the current research interests of faculty and students. Please see the Minimal Learning Outcomes for Math 651.