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Exponential separation in 4–manifolds

Vyacheslav S Krushkal

Geometry & Topology 4 (2000) 397–405

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, $\pi_1$–null immersions, link homotopy
Mathematical Subject Classification 2000
Primary: 57N13
Secondary: 57M25, 57N35, 57N70
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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
Vyacheslav S Krushkal
Department of Mathematics
Yale University
New Haven
Connecticut 06520-8283
USA