**Lisa Piccirillo**

*Knot Theory and 4-Manifolds*

Closed smooth 4-manifold topology contains many notoriously difficult problems. Some of those problems become rather more tractable when posed instead about smooth 4-manifolds with boundary. In this course I’ll discuss a few such problems (exotica, geometric simple connectivity, exotic surfaces) and introduce some tools from knot theory and 3-manifold topology which make these relative problems more approachable. We’ll keep an eye on developing tools in the relative setting which may someday help us understand the closed setting. The first lecture is intended to follow Stipshicz’s first lecture, and will survey the requisite handle calculus.

TAs for this course are **Kyle Hayden** (Columbia University) and **Charles Stine **(Brandeis)

Combine lecture notes for all 5 lectures is available here: Piccirillo

## Lecture 1

Lecture notes are available here Piccirillo 1

## Lecture 2

Lecture notes are available here Piccirillo 2

## Lecture 3

Lisa’s notes for the talk are here: Lecture 3

Lecture notes are available here Piccirillo 3

## Lecture 4

Lisa’s notes for the talk are here: Lecture 4

Lecture notes are available here Piccirillo 4

## Lecture 5

Lisa’s notes for the talk are here: Lecture 5

Lecture notes are available here Piccirillo 5