Tagged Questions
3
votes
0answers
55 views
Soft question: why are there non-smooth manifolds?
Topologists are often very good at explaining the geometric intuition behind certain results and programs of research. For instance, the particular interest in 4 manifolds is often explained by ...
3
votes
2answers
119 views
Does Differential Topology or Differential Geometry play a larger role in Chaos Theory?
I'm an undergraduate on somewhat of a time constraint in school. I have room in my remaining schedule for a semester of either Differential Geometry or Differential Topology.
I understand the ...
16
votes
2answers
310 views
Roadmap to study Atiyah-Singer index theorem
I am a physics undergrad and want to pursue a PhD in Math (geometry or topology). I study it almost completely by myself, as the program in my country offers very less flexibility to take non ...
5
votes
2answers
182 views
Why do people care about principal bundles?
I've started to learn a little about principal bundles (in the smooth category) and while I see how notions like connections and curvature are abstracted from the setting of vector bundles and brought ...
1
vote
1answer
175 views
Prerequisite for Differential Topology and/or Geometric Topology
What are the prerequisites to learning both or one of the items?
Consider that one will have done some of the "core" classes like Differential Geometry, Real Analysis, Abstract Algebra and POint-Set ...
1
vote
1answer
147 views
Why don't we have many differential topologist
I am interested in learning differential topology as
Milnor, Guillemin, Pollack, Hirsch, Kosinski, etc.. did it.
However, I am in University of Toronto as an undergraduate
and none of colleges (or ...
1
vote
1answer
137 views
Taking Differential Topology concurrently with Analysis
So I'm trying to finalize my schedule for this semester. I can't decide whether I should enroll in a grad level Differential Topology (Milnor) class or just the undergrad general topology one. The ...
9
votes
5answers
454 views
Software to draw links or knots
I am looking for software that can aid me in drawing knots and links. There are of course (examples) knotplotters all over the web, but they can only draw specific knots.
What I am looking for is the ...
14
votes
2answers
450 views
Why study “curves” instead of 1-manifolds?
In most undergraduate differential geometry courses -- I am thinking of do Carmo's "Differential Geometry of Curves and Surfaces" -- the topic of study is curves and surfaces in $\mathbb{R}^3$. ...
