Title
Covering, Correspondence and Noncommutative Geometry,Used
Delivery time: 8-12 business days (International)
We construct an additive category whose objects are embedded graphs (or in particular knots) in the 3sphere and where morphisms are formal linear combinations of 3manifolds. Our definition of correspondences relies on the Alexander branched covering theorem, which shows that all compact oriented 3manifolds can be realized as branched coverings of the 3sphere, with branched locus an embedded (not necessarily connected) graph. The way in which a given 3manifold is realized as a branched cover is highly not unique. An interesting homology theory for knots and links that we consider here is the one introduced by Khovanov. We recall the basic definition and properties of Khovanov homology and we give some explicit examples of how it is computed for very simple cases such as the Hopf link. We also recall, the construction of the cobordism group for links and for knots and their relation. We then consider the question of constructing a similar cobordism group for embedded graphs in the 3sphere.
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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.
We accept payments with :
Visa, MasterCard, American Express, Paypal, Shopify Payments, Shop Pay and more.