Homotopy, Isotopy, and Light Bulbs!

A talk by Hannah Schwartz '13

 


Mar25
3:30 pm
2021-03-25 15:30:00 2021-03-25 15:30:00 Homotopy, Isotopy, and Light Bulbs!

Zoom Link: https://occidental.zoom.us/j/97665772888 
Passcode: 788266

Topologists use various notions of equivalence in order to compare curves and surfaces in space. We will discuss two of these in particular: a simple form of equivalence called homotopy, and a strictly stronger form of equivalence called isotopy. In what spaces are these two equivalences the same, i.e. when does homotopy imply isotopy? When are they different? After setting up some necessary background, we will explore recent examples and results about knotted curves and surfaces in both 3 and 4-dimensional spaces that attempt to answer these questions.

America/Los_Angeles public
Event Date: Thursday, March 25, 2021

Zoom Link: https://occidental.zoom.us/j/97665772888 
Passcode: 788266

Topologists use various notions of equivalence in order to compare curves and surfaces in space. We will discuss two of these in particular: a simple form of equivalence called homotopy, and a strictly stronger form of equivalence called isotopy. In what spaces are these two equivalences the same, i.e. when does homotopy imply isotopy? When are they different? After setting up some necessary background, we will explore recent examples and results about knotted curves and surfaces in both 3 and 4-dimensional spaces that attempt to answer these questions.

Sponsored by: Mathematics
Hannah Schwartz