Seeing Four dimensional Space And Beyond Using Knots is popular PDF and ePub book, written by Eiji Ogasa in 2023-07-21, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Seeing Four dimensional Space And Beyond Using Knots can be Read Online from any device for your convenience.
Seeing Four dimensional Space And Beyond Using Knots Book PDF Summary
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.
Detail Book of Seeing Four dimensional Space And Beyond Using Knots PDF
- Author : Eiji Ogasa
- Release : 21 July 2023
- Publisher : World Scientific
- ISBN : 9789811275166
- Genre : Mathematics
- Total Page : 173 pages
- Language : English
- PDF File Size : 15,8 Mb
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