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Семинар им. П.К. Рашевского по тензорному и векторному анализу с приложениями к геометрии, механике и физике
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[Describing Knotted Surfaces, and Constructing Invariants] , Скотт Картер Факультет математики и статистики, Университет Южной Алабамы |
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Аннотация: Most of this talk is a broad review of material found in other sources including books with Saito and Kamada. I'll bring a lot of the material up to date with a fresh look at movies and charts. A detailed discussion of movie-moves would take too long, but some of these isotopies will be illustrated within the context of the talk. I'll show how a 2-dimensional diagram of a graph with certain vertices and labels on edges can be used to describe a knotted surface in 4-dimensional space. I'll also discuss a method of assigning color vectors to regions in such a way that invariants that are associated to the fundamental group are computed. Many examples of non-orientable surfaces will be given. Язык доклада: английский |
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