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  1. ; ; (, Bulletin of the London Mathematical Society)
    Abstract The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 in [Freedman, Kitaev, Nayak, Slingerland, Walker, and Wang, J. Geom. Topol.9(2005), 2303–2317]. We prove an analogous result for 2‐complexes, and show that the universal pairing does not detect the difference between simple homotopy equivalence and 3‐deformations. The question of whether these two equivalence relations are different for 2‐complexes is the subject of the Andrews–Curtis conjecture. We also discuss the universal pairing for higher dimensional complexes and show that it is not positive. 
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