Volume 22, issue 5 (2018)

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On the unstable intersection conjecture

Michael Levin

Geometry & Topology 22 (2018) 2511–2532

Compacta X and Y are said to admit a stable intersection in n if there are maps f : X n and g: Y n such that for every sufficiently close continuous approximations f: X n and g: Y n of f and g, we have f(X) g(Y ). The unstable intersection conjecture asserts that X and Y do not admit a stable intersection in n if and only if dimX × Y n 1. This conjecture was intensively studied and confirmed in many cases. we prove the unstable intersection conjecture in all the remaining cases except the case dimX = dimY = 3, dimX × Y = 4 and n = 5, which still remains open.

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cohomological dimension, extension theory
Mathematical Subject Classification 2010
Primary: 55M10
Secondary: 54F45, 55N45
Received: 19 November 2015
Revised: 19 October 2017
Accepted: 1 November 2017
Published: 1 June 2018
Proposed: Steve Ferry
Seconded: Peter Teichner, David Gabai
Michael Levin
Department of Mathematics
Ben Gurion University of the Negev
Be’er Sheva