Transfinite Milnor invariants for 3-manifolds

  • Jae Choon Cha

    Pohang University of Science and Technology, South Korea
  • Kent E. Orr

    Indiana University, Bloomington, USA
Transfinite Milnor invariants for 3-manifolds cover

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In his 1957 paper, John Milnor introduced link invariants which measure the homotopy class of the longitudes of a link relative to the lower central series of the link group. Consequently, these invariants determine the lower central series quotients of the link group. This work has driven decades of research with profound influence. One of Milnor’s original problems remained unsolved: to extract similar invariants from the transfinite lower central series of the link group. We reformulate and extend Milnor’s invariants in the broader setting of 3-manifolds, with his original invariants as special cases. We present a solution to Milnor’s problem for general 3-manifold groups, developing a theory of transfinite invariants and realizing nontrivial values.

Cite this article

Jae Choon Cha, Kent E. Orr, Transfinite Milnor invariants for 3-manifolds. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1328