%0 Journal Article %J Commun. Math. Phys. 263 (2006) 65-88 %D 2006 %T A Hopf bundle over a quantum four-sphere from the symplectic group %A Giovanni Landi %A Chiara Pagani %A Cesare Reina %X We construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$. %B Commun. Math. Phys. 263 (2006) 65-88 %G en_US %U http://hdl.handle.net/1963/2179 %1 2065 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T12:11:37Z\\nNo. of bitstreams: 1\\n0407342v2.pdf: 282873 bytes, checksum: e4341c8c3cce9ea132fe6c6916a61526 (MD5) %R 10.1007/s00220-005-1494-3