Abstract
A Kauffman state σ of a link diagram D is a choice of resolution for each crossing of D. The resulting surface Sσ is called the state surface of σ. The boundaries of the disks induce a decomposition of the plane into connected components that we call regions. The well known Seifert surface of an oriented diagram of a link is a particular case of a state surface, where the resolution of each crossing is defined by the orientation. It has been an interest of research to identify fibered knots and their fibers. We are interested in understanding when a state surface is a fiber. In the work of Futer, Kalfagianni and Purcell [1, 2] it was studied for homogeneous states, that is when all resolutions of the diagram in each region are the same. (See Theorem 2.)
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
