Knots in ℝP^3
arxiv(2024)
Abstract
The paper studies knots in three dimensional projective space. Our technique
for this purpose is to associate a virtual link to a link in projective space
so that equivalent projective links go to equivalent virtual links (modulo a
special flype move). We can then apply techniques in virtual knot theory to
obtain a Jones polynomial for projective links that is equivalent to the known
Jones polynomial for them and to apply virtual Khovanov homology and the
virtual Rasmussen invariant of Dye, Kaestner, and Kauffman to projective links.
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