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Department of Mathematics

Volume 11 (2007) No. 2

Volume 11 (2007) No. 2 imagen

Hodge structures in non-commutative geometry

Maxim Kontsevich


XI Solomon Lefschetz Memorial Lecture Series, Department of Mathematics, CINVESTAV, 2005. Notes by Ernesto Lupercio.

Traditionally, Hodge structures are associated with complex projective varieties. In my expository lectures I discussed a non-commutative generalization of Hodge structures in deformation quantization and in derived algebraic geometry.


A stringy product on twisted orbifold $K$-theory

Alejandro Adem, Yongbin Ruan, and Bin Zhang


In this paper we define an associative stringy product for the twisted orbifold $K$-theory of a compact, almost complex orbifold $\mathcal{X}$. This product is defined on the twisted $K$-theory $K_{orb}(\wedge \mathcal{X})$ of the inertia orbifold $\wedge \mathcal{X}$, where the twisting gerbe is assumed to be in the image of the inverse transgression $H^4(B \mathcal{X}, \mathbb{Z}) \to H^3 (B \wedge \mathcal{X}, \mathbb{Z})$.