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Winding around: the winding number in topology, geometry, and analysis

The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has fa...

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Detalles Bibliográficos
Autor principal: Roe, John
Lenguaje:eng
Publicado: American Mathematical Society 2015
Materias:
Acceso en línea:http://cds.cern.ch/record/2264092
Descripción
Sumario:The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can help us show that every polynomial equation has a root (the fundamental theorem of algebra), guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem), explain why ever