Browsing by Author "Landi, Giovanni"

Now showing 1 - 3 of 3
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    Families of Monads and Instantons from a Noncommutative ADHM Construction
    (2009-02-03T16:03:43Z) Brain, Simon; Landi, Giovanni; Mathematics; Mathematical Physics
    We 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.
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    The Gysin Sequence for Quantum Lens Spaces
    (2014-01-27) Arici, Francesca; Brain, Simon; Landi, Giovanni; Mathematics
    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.
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    Pimsner algebras and Gysin sequences from principal circle actions
    (2014-03-03) Arici, Francesca; Kaad, Jens; Landi, Giovanni; ; Mathematics
    A self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O_E is then the total space algebra of a noncommutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O_E and of B. Interesting examples come from O_E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.