2-polyhedra for which every homotopy domination over itself is a homotopy equivalence

摘要

We consider an open question: Is it true that each homotopy domination of a polyhedron over itself is a homotopy equivalence? The answer is known to be positive for 1-dimensional polyhedra and polyhedra with virtually-polycyclic fundamental groups, so it is natural to ask about 2-dimensional polyhedra, in particular about those with solvable fundamental groups.