Titlebook: Knots, Low-Dimensional Topology and Applications; Knots in Hellas, Int Colin C. Adams,Cameron McA. Gordon,Radmila Sazdano Conference procee

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Algebraic and Computational Aspects of Quandle 2-Cocycle Invariant,and identities satisfied by quandles induce subcomplexes of homology theory. Recent developments in these matters, as well as computational aspects of the invariant, are reviewed. Problems and conjectures pertinent to the subject are also listed.

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On the Geometry of Some Braid Group Representations,presentations able to detect Brunnian and nested Brunnian phenomena. Physically motivated unitary representations of Riemann surface braid groups are then described, relying on Bellingeri’s presentation and on the geometry of Hermitian–Einstein holomorphic vector bundles on Jacobians, via representations of Weyl-Heisenberg groups.

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2194-1009 Research in new directions, new tools and methods.This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications.?.The focal topics include the wide range of historical and c

Ruptured-Disk

A Survey of Hyperbolic Knot Theory,used to estimate geometric invariants in terms of basic diagrammatic link invariants. We focus on determining when a link is hyperbolic, estimating its volume, and bounding its cusp shape and cusp area. We give sample applications and state some open questions and conjectures.

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Virtual Knot Theory and Virtual Knot Cobordism,rminations of the four-ball genus of positive virtual knots are explained in relation to joint work with Dye and Kaestner [.]. We study the affine index polynomial [.], prove that it is a concordance invariant, show that it is invariant also under certain forms of labeled cobordism and study a numbe

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,Knot Theory: From Fox 3-Colorings of Links to Yang–Baxter Homology and Khovanov Homology,heory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R. Llull (1232–1315), A. Kircher (1602–1680), Leibniz idea of Geometria Situs (1679), and J.B. Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913–1973) elementary int