On the equivalence of suspensions over Cartesian products of regular homeomorphisms with Denjoy homeomorphisms

Homeomorphisms of topological spaces are called suspension equivalent if the suspensions over them are topologically equivalent. In particular, two topologically conjugate homeomorphisms are suspension equivalent. For homologically irreducible homeomorphisms it is known that their topological conjugacy is necessary and sufficient for their suspension equivalence. On the other hand invariants of topological conjugacy of homologically reducible homeomorphisms are often superfluous for suspension equivalence. In particular, such phenomena are characteristic for orientation-preserving circle homeomorphisms because they are homologically reducible. Relations between invariants of topological conjugacy and suspension equivalence are obtained for Denjoy homeomorphisms and their Cartesian products with regular circle homeomorphisms. When the regular homeomorphism reverses orientation, the invariants obtained coincide, while there exist a countable number of pairwise nonconjugate Denjoy homeomorphisms with equivalent suspensions. A similar result is established for the Cartesian products of orientation-preserving regular circle homeomorphisms with Denjoy homeomorphisms. Bibliography: 13 titles.