SKU: 74898457190

Seeing Four-Dimensional Space and Beyond: Using Knots!

Sale price$76.30 Regular price$84.78
Save 10%

Pay in installments of $21.20 with ShopPay, AfterPay and Klarna

Shipping Estimate
USA
  • USA
  • CAN

Ships within 48 hours · Estimated delivery Aug 25 - Aug 30

Promo Codes Available:

For Your Every Summer RSVP, with Code: SUMMER15

Description

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

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.

Shipping Notes
  • Free Standard Shipping on $100+ Orders to the USA.
  • Except Preorder products are shipped in 48 hours.
  • Delivery to the USA:
  1. Standard Shipping : 3-10 business days
  • If time is of the essence, please consider selecting expedited delivery for faster service.
Exchange/Return Notes
  • We offer a 30-day return/exchange service after receiving.
  • Final sale items are not eligible for returns or exchanges.
  • To process your return/exchange, please contact us at [email protected]
  • Please click here for more details>>> Return & Exchange Policy
SKU: 74898457190

Discover Niche Categories That Outsell

Top-Converting Item to Boost Your Average Order

4.0 ★★★★★
Based on 20 reviews
Sort
Highest Rating
Newest First
Oldest First
Product Reviews
M
Verified Purchase
Mandy
Louisville, US
★★★★★ 5
Great quality for value
Style: Cap & Heat Press Bundle
Full set of items you need to start creating fun stuff. Price point is great for everything you get as well as the quality of the items.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on June 7, 2026
C
Verified Purchase
Cheryl Marz
Belleville, US
★★★★★ 4
Loving it
Style: Cap & Heat Press Bundle
The printer is a really good one. After several attempt to get a really good print, I found out you have to have a png design saved at at least a 300 resolution. The heat press seems good but after ruining two kids shirts because I had it set to hot and the pressure was down instead of up so I was applying too much pressure and then trying to figure out why there was blue all over the shirts, I realized the blue silicone pad is what's leaving blue all over the shirts. To combat that I put parchment paper hanging clear down over all edges under the shirt, in the shirt then over the top of the design on the shirt. Finally I had success. I don't know if the company has better silicone pads but this one isn't that good if it bleeds all over.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on November 23, 2024
S
Verified Purchase
SalinasWeddingstuff
Massapequa, US
★★★★★ 5
Subliminal package
Style: Cap & Heat Press Bundle
It works great
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on September 30, 2025
E
Verified Purchase
EGee
San Leandro, US
★★★★★ 5
If you have a Cricut you need this
Style: Starter Bundle
Just what I needed to compliment my Cricut system. Works great, colors are perfect, set up was a breeze, connected to my wireless instantly. Prints look prefect, not all wonky like some can. Value pack was definitely worth the extra $50.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on February 21, 2026
N
Verified Purchase
Ninfa Velásquez
Chelsea, US
★★★★★ 5
Mi impresora
Style: Starter Bundle
I am very happy with my printer. The print quality is excellent; the colors are vibrant, and the details look crisp. That said, I must admit that I have faced a few challenges when adjusting the tones, but I believe that with a little more practice, I will master them. Overall, it is an investment I highly recommend for anyone looking to get started in the world of sublimation.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on May 6, 2026

recommand products