Inventiones mathematicae

, Volume 97, Issue 1, pp 195–207

The algebraic characterization of the exteriors of certain 2-knots

  • Jonathan A. Hillman

DOI: 10.1007/BF01850660

Cite this article as:
Hillman, J.A. Invent Math (1989) 97: 195. doi:10.1007/BF01850660


We study 2-knots with virtually solvable group by applying recent work of Freedman to the 4-manifolds obtained by surgery on such knots. In particular we show that “Gluck reconstruction” is the only ambiguity in recovering the Cappell-Shaneson knots (as TOP locally flat knots) from their groups alone.

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Jonathan A. Hillman
    • 1
  1. 1.School of Mathematics, Physics, Computing and ElectronicsMacquarie UniversityAustralia