{"product_id":"how-surfaces-intersect-in-space-an-introduction-to-topology-2nd-edition-paperback","title":"How Surfaces Intersect in Space: An Introduction to Topology (2nd Edition) - Paperback","description":"\u003cp\u003eby \u003cb\u003eJ. Scott Carter\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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 Möbius 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.\u003c\/p\u003e \u003cp\u003eIn 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.\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eChapter 5 is completely new!\u003c\/strong\u003e 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.\u003c\/p\u003e \u003cp\u003eChapter 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!\u003c\/p\u003e \u003cp\u003eIn the last chapter higher dimensional spaces are examined from an elementary point of view.\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 338\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.74 x 8.47 x 5.96 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e May 01, 1995\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42105349177479,"sku":"9789810220662","price":58.32,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0601\/2623\/2711\/files\/a5a4f93fce1e4cb1c8d5e7658b1ff211.webp?v=1732433651","url":"https:\/\/booksby.splitshops.com\/products\/how-surfaces-intersect-in-space-an-introduction-to-topology-2nd-edition-paperback","provider":"Books by splitShops","version":"1.0","type":"link"}