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Surface-Knots in 4-Space - An Introduction (Paperback, Softcover reprint of the original 1st ed. 2017)
Loot Price: R3,522
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Surface-Knots in 4-Space - An Introduction (Paperback, Softcover reprint of the original 1st ed. 2017)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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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 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.
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