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Category Archives: Topology
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
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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