Invariants for knots in RP^3

Rama Mishra (IISER Pune)

Abstract: In this talk we will discuss knots and links in real projective 3-space RP^3. There are three broad classes of knots in RP^3 namely: affine knots, non-affine class zero knots, and class one knots. We develop a structure theorem to describe a knot diagram for these knots that helps distinguish affine knots from non-affine ones. We develop a plat closure of spherical braids that give rise to links in RP^3 and prove that all links in RP^3 can be represented in this form. Lastly, we associate a virtual knot diagram to a given knot diagram in RP^3 and use this association to define Invariants. This is joint work with Louis Kauffman and Visakh Narayanan.