Seeing Four Dimensional Space And Beyond
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Seeing Four-dimensional Space And Beyond: Using Knots!
According to string theory, our universe exists in a 10- or 11-dimensional space. However, the idea the space beyond 3 dimensions seems hard to grasp for beginners. This book presents a way to understand four-dimensional space and beyond: with knots! Beginners can see high dimensional space although they have not seen it.With visual illustrations, we present the manipulation of figures in high dimensional space, examples of which are high dimensional knots and n-spheres embedded in the (n+2)-sphere, and generalize results on relations between local moves and knot invariants into high dimensional space.Local moves on knots, circles embedded in the 3-space, are very important to research in knot theory. It is well known that crossing changes are connected with the Alexander polynomial, the Jones polynomial, HOMFLYPT polynomial, Khovanov homology, Floer homology, Khovanov homotopy type, etc. We show several results on relations between local moves on high dimensional knots and their invariants.The following related topics are also introduced: projections of knots, knot products, slice knots and slice links, an open question: can the Jones polynomial be defined for links in all 3-manifolds? and Khovanov-Lipshitz-Sarkar stable homotopy type. Slice knots exist in the 3-space but are much related to the 4-dimensional space. The slice problem is connected with many exciting topics: Khovanov homology, Khovanv-Lipshits-Sarkar stable homotopy type, gauge theory, Floer homology, etc. Among them, the Khovanov-Lipshitz-Sarkar stable homotopy type is one of the exciting new areas; it is defined for links in the 3-sphere, but it is a high dimensional CW complex in general.Much of the book will be accessible to freshmen and sophomores with some basic knowledge of topology.
Seeing Four-dimensional Space and Beyond
"An introductory text for knot theory. Introduces the tool for visualizing 4- and higher-dimensional space. Also discusses recent developments in the field"--
Fear of Seeing
Author: Mingwei Song
language: en
Publisher: Columbia University Press
Release Date: 2023-10-03
Winner, 2023 SFRA Book Award, Science Fiction Research Association A new wave of cutting-edge, risk-taking science fiction has energized twenty-first-century Chinese literature. These works capture the anticipation and anxieties of China’s new era, speaking to a future filled with uncertainties. Deeply entangled with the politics and culture of a changing China, contemporary science fiction has also attracted a growing global readership. Fear of Seeing traces the new wave’s origin and development over the past three decades, exploring the core concerns and literary strategies that make it so distinctive and vital. Mingwei Song argues that recent Chinese science fiction is united by a capacity to illuminate what had been invisible—what society had chosen not to see; what conventional literature had failed to represent. Its poetics of the invisible opens up new literary possibilities and inspires new ways of telling stories about China and the world. Reading the works of major writers such as Liu Cixin and Han Song as well as lesser-known figures, Song explores how science fiction has spurred larger changes in contemporary literature and culture. He analyzes key topics: variations of utopia and dystopia, cyborgs and the posthuman, and nonbinary perspectives on gender and genre, among many more. A compelling and authoritative account of the politics and poetics of contemporary Chinese science fiction, Fear of Seeing is an important book for all readers interested in the genre’s significance for twenty-first-century literature.