Inverse semigroup equivariant KK-theory and C^*-extensions

Equivariant KK-theory and noncommutative index theory

The Universal Property of Equivariant Kk-theory

Let G be a locally compact, σ-compact group. We prove that the equivariant KK-theory, KK, is the universal category for functors from G-algebras to abelian groups which are stable, homotopy invariant and split-exact. This is a generalization of Higsons characterisation of (non-equivariant) KK-theory.

extensions, minimality and idempotents of certain semigroup compactifications

در فصل اول مقدمات و پیش نیازهای لازم برای فصل های بعدی فراهم گردیده است . در فصل دوم مساله توسیع مورد توجه قرار گرفته و ابتدا شرایطی که تحت آن از یک فشرده سازی نیم گروهی خاص یک زیرگروه نرمال بسته یک گروه به یک فشرده سازی متناظر با فشرده سازی اولیه برای گروه رسید مورد بررسی قرار گرفته و سپس ارتیاط بین ساختارهای مختلف روی این دو فشرده سازی از جمله ایده آل های مینیمال چپ و راست و... مورد بررسی قرا...

Equivariant inverse spectral theory and toric orbifolds

Let O be a symplectic toric orbifold with a fixed T-action and with a toric Kähler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace operator ∆g on C∞(O) determines the moment polytope of O, and hence by Delzant’s theorem determines O up to symplectomorphism. In the setting of toric orbifolds we significantly improve upon our previous results a...

Canonical equivariant extensions using classical Hodge theory

In [4], Lin and Sjamaar show how to use symplectic Hodge theory to obtain canonical equivariant extensions of closed forms in Hamiltonian actions of compact connected Lie groups on closed symplectic manifolds which have the strong Lefschetz property. In this paper, we show how to do the same using classical Hodge theory. This has the advantage of applying far more generally. Our method makes us...