## MATH 8750: Topology of Manifolds

Topics include the Whitney trick and its failure in 4 dimensions; its analogues in 3-dimensions: the Dehn lemma and the loop theorem; Milnor's invariants for classical links; various special 2...

Content

Semester

Fall

Year offered

2019

Topics include the Whitney trick and its failure in 4 dimensions; its analogues in 3-dimensions: the Dehn lemma and the loop theorem; Milnor's invariants for classical links; various special 2...

Semester

Spring

Year offered

2019

Course material: Vector bundles, principal bundles, associated bundles, characteristic classes (Stiefel-Whiteney, Chern, Pontryagin). Orientability, Euler class. Classifying spaces (for vector bundles...

Semester

Fall

Year offered

2018

The main goal of the class is to give an introduction to geometric and quantum topology in low (2, 3, 4) dimensions. Specific topics that will be discussed include the (colored) Jones polynomial of...

Semester

Spring

Year offered

2018

This class gives an overview of both classical and modern results in Knot theory: the Kauffman bracket and the Jones polynomial; the Alexander polynomial; Khovanov homology; Seifert surfaces; examples...

Semester

Fall

Year offered

2017

Semester

Spring

Year offered

2017

Topics include: manifolds, the Gauss map, parallel transport, curvature of curves and surfaces, the first and second fundamental forms, surface area and volume, geodesics, the exponential map, the...

Semester

Spring

Year offered

2017

Semester

Fall

Year offered

2016

Topics covered in this class include analytic functions, complex integration, Cauchy formulas, power series, residue theory, conformal mappings, and Laplace transforms.

Semester

Spring

Year offered

2016

Semester

Spring

Year offered

2016

Semester

Fall

Year offered

2015

Semester

Spring

Year offered

2015

Semester

n/a

Year offered

2014

Semester

Fall

Year offered

2013

Semester

Fall

Year offered

2013