03252nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118040002500153050001400178072001600192072002300208072001500231082001200246100007800258245009300336264006500429300004400494336002600538337002600564338003600590347002400626490005100650505029100701520119900992650001402191650002402205650003502229650008502264650009502349650012702444710003402571773002002605776003602625776003602661830005102697856004602748978-981-10-4091-7DE-He21320181204134419.0cr nn 008mamaa170328s2017 si | s |||| 0|eng d a97898110409177 a10.1007/978-981-10-4091-72doi aISI Library, Kolkata 4aQA440-699 7aPBM2bicssc 7aMAT0120002bisacsh 7aPBM2thema04a5162231 aKamada, Seiichi.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aSurface-Knots in 4-Spaceh[electronic resource] :bAn Introduction /cby Seiichi Kamada. 1aSingapore :bSpringer Singapore :bImprint: Springer,c2017. aXI, 212 p. 146 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aSpringer Monographs in Mathematics,x1439-73820 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. 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. 0aGeometry. 0aAlgebraic topology. 0aCell aggregationxMathematics.14aGeometry.0http://scigraph.springernature.com/things/product-market-codes/M2100624aAlgebraic Topology.0http://scigraph.springernature.com/things/product-market-codes/M2801924aManifolds and Cell Complexes (incl. Diff.Topology).0http://scigraph.springernature.com/things/product-market-codes/M280272 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978981104090008iPrinted edition:z9789811040924 0aSpringer Monographs in Mathematics,x1439-738240uhttps://doi.org/10.1007/978-981-10-4091-7