About: Capped grope

In mathematics, a grope is a construction used in 4-dimensional topology, introduced by and named by "because of its multitudinous fingers". Capped gropes were used by as a substitute for Casson handles, that work better for non-simply-connected 4-manifolds. A capped surface in a 4-manifold is roughly a surface together with some 2-disks, called caps, whose boundaries generate the fundamental group of the surface. A capped grope is obtained by repeatedly replacing the caps of a capped surface by another capped surface. Capped surfaces and capped gropes are studied in .