01003nas a2200133   4500008004300000245004600043210004300089260001300132520062600145100002200771700002000793700002000813856003600833       2001                        en_Ud  00aInstantons on the Quantum 4-Spheres S^4_q0 aInstantons on the Quantum 4Spheres S4q  bSpringer3 aWe introduce noncommutative algebras $A_q$ of quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IR$, defined via a suspension of the quantum group $SU_q(2)$, and a quantum instanton bundle described by a selfadjoint idempotent $e\\\\in \\\\Mat_4(A_q)$, $e^2=e=e^*$. Contrary to what happens for the classical case or for the noncommutative instanton constructed in Connes-Landi, the first Chern-Connes class $ch_1(e)$ does not vanish thus signaling a dimension drop. The second Chern-Connes class $ch_2(e)$ does not vanish as well and the couple $(ch_1(e), ch_2(e))$ defines a cycle in the $(b,B)$ bicomplex of cyclic homology.1 aDabrowski, Ludwik1 aLandi, Giovanni1 aMasuda, Tetsuya  uhttp://hdl.handle.net/1963/3135