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100   $a20170328d2017      u|             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aSurface-knots in 4-space$b[electronic resource] $ean introduction /$fby Seiichi Kamada
205   $a1st ed. 2017.
210  1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2017.
215   $a1 online resource (XI, 212 p. 146 illus.)
225 1 $aSpringer Monographs in Mathematics,$x1439-7382
311   $a981-10-4090-7 
320   $aIncludes bibliographical references and index.
327   $a1 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.
330   $aThis introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field. Knot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval. Included in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surface diagrams, handle surgeries, ribbon surface-knots, spinning construction, knot concordance and 4-genus, quandles and their homology theory, and two-dimensional braids.
410  0$aSpringer Monographs in Mathematics,$x1439-7382
606   $aGeometry
606   $aAlgebraic topology
606   $aManifolds (Mathematics)
606   $aComplex manifolds
606   $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006
606   $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019
606   $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027
615  0$aGeometry.
615  0$aAlgebraic topology.
615  0$aManifolds (Mathematics).
615  0$aComplex manifolds.
615 14$aGeometry.
615 24$aAlgebraic Topology.
615 24$aManifolds and Cell Complexes (incl. Diff.Topology).
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700   $aKamada$b Seiichi$4aut$4http://id.loc.gov/vocabulary/relators/aut$0734235
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