State cycles which represent the canonical class of Lee's homology of a knot

摘要

For a diagram of a knot. Lee associated a complex which is called Lee's complex. We introduce the notion of a state cycle of Lee's complex, which is a certain cycle of Lee's complex. We describe state cycles which represent the canonical class of Lee's homology of a knot. As a corollary, we give the shaper slice-Bennequin inequality for the Rasmussen invariant of a knot in the viewpoint of cycles of Lee's complex.