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Right-angled volume of alternating links

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Abhijit Champanerkar (CUNY)

Abstract: To any prime alternating link, we associate a collection of hyperbolic right-angled ideal polyhedra by relating geometric, topological and combinatorial methods to decompose the link complement. The sum of the hyperbolic volumes of these polyhedra is a new geometric link invariant, which we call the right-angled volume of the alternating link. We give an explicit procedure to compute the right-angled volume from any alternating link diagram, and prove that it is a new lower bound for the hyperbolic volume of the link. We will discuss recent results in computational graph theory which give an algorithm to compute this volume. Lastly, we will discuss related open questions. This is joint work with Ilya Kofman and Jessica Purcell.