A homological Casson type invariant of knotoids (Q2041222)

The Casson invariant is originally defined as an integer-valued invariant for oriented integral homology 3-spheres. It also determines an invariant of knots that are embedded in integral homology 3-spheres. This paper considers an analog of the Casson knot invariant for knotoids (open-ended knot diagrams with a special assumption on the endpoints) in surfaces, and extends the notion to the homology case. The paper also consists of results relating the Casson invariant to crossing number of knotoids.