Capped grope

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4-dimensional topology, introduced by Štan'ko (1971) and named by Cannon (1978) "because of its multitudinous fingers". Capped gropes were used by Freedman (1984) as a substitute for Casson handles, that[vague] work better for non-simply-connected 4-manifolds
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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 Freedman & Quinn (1990).

References

  • Cannon, J. W. (1978), "The recognition problem: what is a topological manifold?",
    MR 0494113
  • MR 0804721
  • MR 1201584
  • Štan'ko, M. A. (1971), "Approximation of the imbedding of compacta in a codimension larger than two", Doklady Akademii Nauk SSSR, 198: 783–786,
    MR 0284994
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