Geometry & Topology, Vol. 4 (2000) Paper no. 13, pages 397--405.

Exponential separation in 4-manifolds

Vyacheslav S Krushkal

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 pi_1-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

AMS subject classification. Primary: 57N13. Secondary: 57M25, 57N35, 57N70.

DOI: 10.2140/gt.2000.4.397

E-print: arXiv:math.GT/0008212

Submitted to GT on 27 June 2000. Paper accepted 3 November 2000. Paper published 10 November 2000.

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Vyacheslav S Krushkal
Department of Mathematics, Yale University
New Haven, CT 06520-8283, USA

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