2022/05/14 by Andrew Bartholomew, Roger Fenn
Mathematics · Biochemistry, Genetics and Molecular Biology · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Connective tissue disorders research
paper · doi:10.1142/s0218216522400107
In the first of this series of papers, we looked at various generalized knot theories. In this follow up paper, we look at the theory of generalized braids and show how they are related to generalized knots. The twin groups are related to the theory of planar doodles and we prove a Markov-type theorem for them. An example and invariants are given to show that this is best possible. We also give conditions for when an exchange move is dependent on the other moves.