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**1 - 5**of**5**### Motivic structures in non-commutative geometry. Available at arXiv:1003.3210

- the Proceedings of the ICM
, 2010

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### Introduction to motives

"... This article is based on the lectures of the same tittle given by the first author during ..."

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This article is based on the lectures of the same tittle given by the first author during

### 2.2.6 The Q-structure............................ 31

"... 2.4.1 A quiver description of nc-Betti data............... 45 ..."

### Bordered Heegaard Floer . . .

, 2008

"... We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented two-manifold a differential graded algebra. For a three-manifold with specified boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra ..."

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We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented two-manifold a differential graded algebra. For a three-manifold with specified boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A ∞ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A∞ tensor product of the type D module of one piece and the type A module from the other piece is ̂ HF of the glued manifold. As a special case of the construction, we specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for ̂ HF. We relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

### THE EQUIVARIANT PAIR-OF-PANTS PRODUCT IN FIXED POINT FLOER COHOMOLOGY

"... The constructions in this paper are modelled on ones in equivariant cohomology, and we therefore start with a quick review of that theory (specialized to the group Z/2). After that, we explain the main new result (Theorem 1.4), and some of its implications for fixed point Floer cohomology. Returning ..."

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The constructions in this paper are modelled on ones in equivariant cohomology, and we therefore start with a quick review of that theory (specialized to the group Z/2). After that, we explain the main new result (Theorem 1.4), and some of its implications for fixed point Floer cohomology. Returning to the general picture, we will conclude the introductory