Original scientific paper
https://doi.org/10.21857/yvjrdcdjly
A Hurewicz-type formula for asymptotic-dimension-lowering symmetric quasimorphisms of countable approximate groups
Vera Tonić
; Faculty of Mathematics, University of Rijeka, 51 000 Rijeka, Croatia
Abstract
A well-known Hurewicz-type formula for asymptotic-dimension-lowering group homomorphisms, due to A. Dranishnikov and J. Smith, states that if f : G → H is a group homomorphism, then asdim G ≤ asdim H + asdim (ker f). In this paper we establish a similar formula for certain quasimorphisms of countable approximate groups: if (Ξ, Ξ∞) and (Λ, Λ∞) are countable approximate groups and if f : (Ξ, Ξ∞) → (Λ, Λ∞) is a symmetric unital quasimorphism, we show that asdim Ξ ≤ asdim Λ + asdim (f -1(D(f))), where D(f) is the defect set of f.
Keywords
Asymptotic dimension; approximate group; quasimorphism
Hrčak ID:
326528
URI
Publication date:
9.1.2025.
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