{"product_id":"9789811040900","title":"Surface-Knots in 4-Space","description":"\u003cdiv\u003eThis introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.\u003c\/div\u003e\u003cdiv\u003eKnot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval.\u003c\/div\u003e\u003cdiv\u003eIncluded in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surface diagrams, handle surgeries, ribbon surface-knots, spinning construction, knot concordance and 4-genus, quandles and their homology theory, and two-dimensional braids.\u003c\/div\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ePublication Year: \u003c\/strong\u003e2017\u003cbr\u003e\u003cstrong\u003eImprint: \u003c\/strong\u003eSpringer Singapore\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003eFormat: H\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003eWeight (Gram): 4616\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/p\u003e","brand":"Seiichi Kamada","offers":[{"title":"Default Title","offer_id":41246274126002,"sku":"9789811040900","price":148.19,"currency_code":"SGD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0502\/5382\/4178\/products\/9811040907.01_SCLZZZZZZZ.jpg?v=1635643896","url":"https:\/\/readabook.store\/products\/9789811040900","provider":"READABOOK BY ALKEM","version":"1.0","type":"link"}