Title
Hyperbolic Knots with distance3 Toroidal Surgeries in S: Examples and Characterization,Used
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By the work of Thurston, any surgery on a hyperbolic knot in the 3sphere produces a hyperbolic 3manifold except in at most finitely many cases. So far, the figure8 knot seems to be the best candidate for a hyperbolic knot with the most (8) nontrivial exceptional surgeries. In recent years, much progress has been made in the classification of hyperbolic knots admitting more than one exceptional toroidal surgery. In fact, such classification is known for toroidal surgeries with distance at least 4. We give a necessary condition for a hyperbolic knot in the 3sphere admitting two toroidal surgeries at distance 3, whose slopes are represented by twice punctured essential separating tori. Namely, such knots belong to a family K(a, b, n), where a, b, n are integers and gcd(a, b) = 1. This result should be specially useful for geometers, topologists or anyone else interested in the theory of 3dimensional manifolds.
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Shipping & Returns
Shipping
We ship your order within 2–3 business days for USA deliveries and 5–8 business days for international shipments. Once your package has been dispatched from our warehouse, you'll receive an email confirmation with a tracking number, allowing you to track the status of your delivery.
Returns
To facilitate a smooth return process, a Return Authorization (RA) Number is required for all returns. Returns without a valid RA number will be declined and may incur additional fees. You can request an RA number within 15 days of the original delivery date. For more details, please refer to our Return & Refund Policy page.
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Warranty
We provide a 2-year limited warranty, from the date of purchase for all our products.
If you believe you have received a defective product, or are experiencing any problems with your product, please contact us.
This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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Your payment information is processed securely. We do not store credit card details nor have access to your credit card information.
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