How Surfaces Intersect in Space: An Introduction to TopologyWorld Scientific, 1995 - Всего страниц: 318 This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In the second chapter we are introduced to the M bius band and surfaces that can be constructed from this non-orientable piece of fabric. In chapter 3, we see how curves can fit in surfaces and how surfaces can fit into spaces with these curves on their boundary. Basic applications to knot theory are discussed and four-dimensional space is introduced.In Chapter 4 we learn about some 3-dimensional spaces and surfaces that sit inside them. These surfaces help us imagine the structures of the larger space.Chapter 5 is completely new! It contains recent results of Cromwell, Izumiya and Marar. One of these results is a formula relating the rank of a surface to the number of triple points. The other major result is a collection of examples of surfaces in 3-space that have one triple point and 6 branch points. These are beautiful generalizations of the Steiner Roman surface.Chapter 6 reviews the movie technique for examining surfaces in 4-dimensional space. Various movies of the Klein bottle are presented, and the Carter-Saito movie move theorem is explained. The author shows us how to turn the 2-sphere inside out by means of these movie moves and this illustration alone is well worth the price of the book!In the last chapter higher dimensional spaces are examined from an elementary point of view.This is a guide book to a wide variety of topics. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures. |
Содержание
Surface and Space | 1 |
Other Three Dimensional Spaces | 4 |
Nonorientable Surfaces | 23 |
Curves and Knots | 83 |
Relationships | 173 |
Surfaces in 4Dimensions | 207 |
Higher Dimensional Spaces | 271 |
305 | |
317 | |
Другие издания - Просмотреть все
How Surfaces Intersect in Space: An Introduction to Topology J Scott Carter Ограниченный просмотр - 1993 |
How Surfaces Intersect in Space: An Introduction to Topology J Scott Carter Ограниченный просмотр - 1995 |
How Surfaces Intersect in Space: An Introduction to Topology J. Scott Carter Недоступно для просмотра - 1995 |
Часто встречающиеся слова и выражения
2-handle 2-sphere 3-dimensional space 3-sphere 4-dimensions algebraic annulus arcs of double ball basket shaped thingy belt sphere boundary circles boundary components bounds a disk Boy's surface branch points Cartesian product Chapter closed surface consider constructed coordinate disks critical points cut-line deformation dimension disk bounded disk in 4-space double arc double decker arcs double points equator equatorial Euler number example Gauss word genus given glued handle decomposition handle slides higher dimensional homeomorphism Hopf link immersed indicates inside intersecting disks invariant Jordan Curve Theorem JSC Figure Klein bottle knot diagram lens space loop manifold Marar Masahico Möbius band movie moves n-manifold neighborhood non-orientable surface number of boundary orientable surfaces pair of mates planar surface preimage projective plane projective space quotient rank Reidemeister moves Roman surface rotation separate sequence simple closed curve slice smoothing solid torus substantial arc substantial circles surface with boundary topology triangles triple point unknot vertex
Ссылки на эту книгу
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