
The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society
Subscribe to Blog via Email
Comics

Recent Posts
Recent Comments
 Behnam Esmayli on Intersection of a Chain of Subsets
 Brandon on Intersection of a Chain of Subsets
 Behnam Esmayli on Applying to grad school? Here’s what you need to know: Part II
 Fatimah on Riddle of the Month (October)
 fluxxdog on Riddle of the Month (October)
Archives
Categories

Comments Guidelines
The AMS encourages your comments, and hopes you will join the discussions. We review comments before they're posted, and those that are offensive, abusive, offtopic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.
Meta
Tag Archives: Topology
Real Numbers Base…Factorials! And A Byproduct
PROPOSITION 1: For a real number x there exists a sequence $ x_1, x_2, x_3,…$ of integers such that $ \hspace{4cm} x=x_1 +\frac{x_2}{2!}+\frac{x_3}{3!} + \cdots + \frac{x_n}{n!} + \cdots, \hspace{2cm} (*) $ where $x_1$ can be any integer, but for … Continue reading
Gauge Theory and LowDimensional Topology (Part II: Smooth FourManifolds)
In the last post, I attempted to give an overview of the state of affairs in fourmanifold topology leading up to the introduction of gauge theory. In particular, we discussed the correspondence between (topological) fourmanifolds and their intersection forms afforded by … Continue reading
Donaldson Turns 60
“Donaldson has opened up an entirely new area; unexpected and mysterious phenomena about the geometry of 4dimensions have been discovered. Moreover, the methods are new and extremely subtle, using difficult nonlinear partial differential equations. On the other hand, this theory … Continue reading
Posted in Algebraic Geometry, Math, Topology
Tagged Differential Geometry, Math, Topology
Leave a comment
Gauge Theory and LowDimensional Topology (Part I: Historical Context)
Hi! This month, I thought I would start a brief series of articles describing the uses of gauge theory in mathematics. Rather than discuss current research directions in gauge theory (of which there are many), I hope to give an … Continue reading
What is a Manifold? (6/6)
In posts 13 we were able to reduce all of the geometry of a curve in 3space to an interval along with two or three realvalued functions. We also discussed when two sets of such data give equivalent (overlapping) curves. This … Continue reading