Abstract

ABSTRACTWe review some our results concerning the topology of knotted and linked defects in nematic liquid crystals. We discuss the global topological classification of nematic textures with defects, showing how knotted and linked defect lines have a finite number of ‘internal states’, counted by the Alexander polynomial of the knot or link. We then give interpretations of these states in terms of umbilic lines, which we also introduce, as well as planar textures. We show how Milnor polynomials can be used to give explicit constructions of these textures. Finally, we discuss some open problems raised by this work.

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

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.