#### Volume 4, issue 1 (2000)

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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 ${\pi }_{1}$–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
##### Mathematical Subject Classification 2000
Primary: 57N13
Secondary: 57M25, 57N35, 57N70