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＜電子ブック＞
Surface-Knots in 4-Space : An Introduction / by Seiichi Kamada
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2017.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2017
本文言語	英語
大きさ	XI, 212 p. 146 illus : online resource
著者標目	*Kamada, Seiichi author SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Algebraic topology LCSH:Manifolds (Mathematics) FREE:Geometry FREE:Algebraic Topology FREE:Manifolds and Cell Complexes
一般注記	1 Surface-knots -- 2 Knots -- 3 Motion pictures -- 4 Surface diagrams -- 5 Handle surgery and ribbon surface-knots -- 6 Spinning construction -- 7 Knot concordance -- 8 Quandles -- 9 Quandle homology groups and invariants -- 10 2-Dimensional braids -- Bibliography -- Epilogue -- Index This 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. Knot 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. Included in this book are basics of surface-knots and the related topics ofclassical 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 HTTP:URL=https://doi.org/10.1007/978-981-10-4091-7

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