Baek Seongha and Cha Kihyun share the outfield, the glory, and a hotel room on the road. They are the Ulsan Hounds' star Alphas—best friends, teammates, and totally platonic.Until Seongha hits an unexpected Rut.Trapped in a hotel room with no suppressants, Kihyun makes a reckless choice to help his teammate through the fever.

In this partly expository work, a framework is developed for building exotic circle actions of certain classical groups.The authors give general combination theorems for indiscrete isometry groups of hyperbolic space which apply to Fuchsian and limit groups. An abundance of integer-valued subadditive defect-one quasimorphisms on these groups follow as a corollary.The main classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit large colle...