Inequalities for 4-Manifolds with Ends using Fibered boundary metric and Seiberg-Witten Equations

We deduce a new inequality using the Hitchin-Thorpe inequality for noncompact complete four-dimensional manifolds with fibered geometry at infinity and Seiberg-Witten gauge-theoretic techniques. Fibered geometry at infinity is either fibered boundary metric or fibered cusp metric. We prove it for fibered boundary metric when the fiber at boundary is a single point.