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Category Archives: Topology
AMS Notices Spotlight October 2017
Hello and welcome to the October AMS Notices Spotlight. As we are now into the swing of the busyness of the semester it is sometimes nice to take a break and think about math not related to our classes. With … Continue reading
Posted in Algebra, AMS, Mathematics in Society, Topology
Tagged Algebraic Topology, AMS, Notices
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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
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