The work of Vaughan Jones has connected these objects to the Ising model of statistical mechanics, while Dehn's theorem demonstrates that if one of these objects' namesake group is isomorphic to the integers, then the object itself is isomorphic to a closed loop. Dowker nota
The work of Vaughan Jones has connected these objects to the Ising model of statistical mechanics, while Dehn's theorem demonstrates that if one of these objects' namesake group is isomorphic to the integers, then the object itself is isomorphic to a closed loop. Dowker notation can be used to enumerate prime ones, examples of which are the hyperbolic, torus, and satellite types. The determinants of these structures are given by evaluating the Alexander polynmial at negative one, and other invariants related to these objects are the Jones and HOMFLY polynomials. Manipulated by Reidemesiter moves and generalizable in three dimensions to links, for ten points, identify these mathematical objects, examples of which include the bend, trefoil, and pretzel varieties.
The work of Vaughan Jones has connected these objects to the Ising model of statistical mechanics, while Dehn's theorem demonstrates that if one of these objects' namesake group is isomorphic to the integers, then the object itself is isomorphic to a closed loop.
knots