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SEMINARS |
Geometric Topology Seminar
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Introduction to Kirby diagrams of four-manifolds A. C. Lightfoot |
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Abstract: A Kirby diagram is a convenient way to describe a handle decomposition of a four-manifold. It consists of a link in 3-space, where each component is either equipped with an integer, or the component is an unknot with a “dot”. In this talk we will explain the meaning of such a diagram and how to use them to illustrate certain diffeomorphisms between four-manifolds. In relation to the series of talks described below, our particular aim is to exhibit a Kirby diagram for the complement in the 4-sphere of an immersed 2-sphere (or, rather, a regular neighborhood thereof), and use the Kirby diagram to construct certain surfaces in the four-manifold. This is the third in a series of talks in which we give a careful exposition of a recent ground-breaking paper of Rob Schneiderman and Peter Teichner, The Group of Disjoint 2-Spheres in 4-Space, arXiv:1708.00358}. A link map Website: https://arxiv.org/abs/1708.00358
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