We define quantum lens spaces as ‘direct sums of line bundles’ and exhibit them as ‘total spaces’ of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as ‘line bundles’ over quantum lens spaces and generically define ‘torsion classes’. We work out explicit examples of these classes.

1 aArici, Francesca1 aBrain, Simon1 aLandi, Giovanni uhttps://www.math.sissa.it/publication/gysin-sequence-quantum-lens-spaces-001072nas a2200121 4500008004300000245008700043210006900130260002800199520065000227100001700877700002000894856003600914 2012 en_Ud 00aModuli spaces of noncommutative instantons: gauging away noncommutative parameters0 aModuli spaces of noncommutative instantons gauging away noncommu bOxford University Press3 aUsing the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_\\\\theta. We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gauge parameters using a noncommutative quotient construction. Although the parameter spaces are a priori noncommutative, we show that one may always recover a classical parameter space by making an appropriate choice of gauge transformation.1 aBrain, Simon1 aLandi, Giovanni uhttp://hdl.handle.net/1963/377700938nas a2200109 4500008004300000245007800043210006900121520056500190100001700755700002000772856003600792 2009 en_Ud 00aFamilies of Monads and Instantons from a Noncommutative ADHM Construction0 aFamilies of Monads and Instantons from a Noncommutative ADHM Con3 aWe give a \\\\theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative `families\\\' of SU(2) instantons on the deformed sphere S^4_\\\\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.1 aBrain, Simon1 aLandi, Giovanni uhttp://hdl.handle.net/1963/3478