Surface-Knots in 4-Space

An Introduction

Nonfiction, Science & Nature, Mathematics, Topology, Geometry
Cover of the book Surface-Knots in 4-Space by Seiichi Kamada, Springer Singapore
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Seiichi Kamada ISBN: 9789811040917
Publisher: Springer Singapore Publication: March 28, 2017
Imprint: Springer Language: English
Author: Seiichi Kamada
ISBN: 9789811040917
Publisher: Springer Singapore
Publication: March 28, 2017
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Singapore

Cover of the book Teaching Chinese Language in Singapore by Seiichi Kamada
Cover of the book Enterprise Risk Management in International Construction Operations by Seiichi Kamada
Cover of the book Indian Hotspots by Seiichi Kamada
Cover of the book Geotechnics for Natural and Engineered Sustainable Technologies by Seiichi Kamada
Cover of the book Communities of Practice by Seiichi Kamada
Cover of the book Trade Liberalisation, Economic Growth and Environmental Externalities by Seiichi Kamada
Cover of the book Active Tectonics of Kumaun and Garhwal Himalaya by Seiichi Kamada
Cover of the book Building Maintenance Processes and Practices by Seiichi Kamada
Cover of the book Becoming ‘Good Muslim’ by Seiichi Kamada
Cover of the book High Speed Railway Track Dynamics by Seiichi Kamada
Cover of the book Deterritorialised Identity and Transborder Movement in South Asia by Seiichi Kamada
Cover of the book Medicinal Plants - Recent Advances in Research and Development by Seiichi Kamada
Cover of the book Predictive Computing and Information Security by Seiichi Kamada
Cover of the book Waste Water Recycling and Management by Seiichi Kamada
Cover of the book PLD Based Design with VHDL by Seiichi Kamada
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy