On the unstable intersection conjecture

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2 Scopus citations


Compacta X and Y are said to admit a stable intersection in ℝn if there are maps f: X → ℝn and g: Y → ℝn such that for every sufficiently close continuous approximations f': X → ℝn and g': Y → ℝn 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 ℝn if and only if dim X × 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 dim X = dim Y = 3, dim X × Y = 4 and n = 5, which still remains open.

Original languageEnglish
Pages (from-to)2511-2532
Number of pages22
JournalGeometry and Topology
Issue number5
StatePublished - 1 Jun 2018


  • Cohomological dimension
  • Extension theory

ASJC Scopus subject areas

  • Geometry and Topology


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