Surface-Knots in 4-Space

An Introduction

Seiichi Kamada (Autor)

Buch | Softcover

212 Seiten

2018 | Softcover reprint of the original 1st ed. 2017
Springer Verlag, Singapore
978-981-13-5046-7 (ISBN)

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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.

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.

Erscheinungsdatum	04.03.2022
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	146 Illustrations, black and white; XI, 212 p. 146 illus.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	2-dimensional braid • Motion picture • Quandle and quandle homology • Surface diagram • Surface knot
ISBN-10	981-13-5046-9 / 9811350469
ISBN-13	978-981-13-5046-7 / 9789811350467
Zustand	Neuware