Geometry & Topology 4 (2000) 397–405

DOI: 10.2140/gt.2000.4.397

arXiv: math.GT/0008212

Abstract

We use a new geometric construction, grope splitting, to give a sharp bound for separation of surfaces in 4–manifolds. We also describe applications of this technique in link-homotopy theory, and to the problem of locating π₁–null surfaces in 4–manifolds. In our applications to link-homotopy, grope splitting serves as a geometric substitute for the Milnor group.

Keywords

4–manifolds, gropes, π₁–null immersions, link homotopy

Mathematical Subject Classification

Primary: 57N13

Secondary: 57M25, 57N35, 57N70

References

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Publication

Received: 27 June 2000
Accepted: 3 November 2000
Published: 10 November 2000
Proposed: Robion Kirby
Seconded: Wolfgang Metzler, Cameron Gordon

Authors