Let G be an irreducible uniform lattice in a higher semi-simple rank Lie group or algebraic group. We prove that any G-action on the circle by C1 diffeomorphisms is finite. This is achieved by showing that natural map from bounded to usual second cohomology is injective. The latter holds also for non-trivial unitary coefficients, and implies more finiteness results for G; for instance the stable commutator length vanishes. We prove the same theorems for certain lattices in products of trees.

https://egg.epfl.ch/~nmonod/articles/jems.pdf

Bounded cohomology of lattices in higher rank Lie groups

Using the L2 norm of the Higgs field as a Morse function, we study the moduli spaces of U(p, q)-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no constraints on (p, q). A key step is the identification of the function's local minima as moduli spaces of holomorphic triples. In a companion paper [7] we prove that these moduli spaces of triples are nonempty and irreducible. Because of the relation between flat bundles and fundamental group representations, we can interpret our conclusions as results about the number of connected components in the moduli space of semisimple PU(p, q)-representations. The topological invariants of the flat bundles are used to label subspaces. These invariants are bounded by a Milnor–Wood type inequality. For each allowed value of the invariants satisfying a certain coprimality condition, we prove that the corresponding subspace is nonempty and connected. If the coprimality condition does not hold, our results apply to the closure of the moduli space of irreducible representations.

/pdf/surface-group-representations-and-u-p-q-higgs-bundles-1mhawouss7.pdf

Surface group representations and U(p, q)-Higgs bundles

Nous esperons avoir convaincu le lecteur qu'il peut etre utile de considerer la classe de Maslov comme une classe bornee. Dans [Gh], nous avons montre que la classe d'Euler bornee pour un groupe d'homeomorphismes directs du cercle rend compte de la dynamique topologique de ce groupe. Existe-t-il un resultat analogue pour Sp(2n,ℝ)? En d'autres termes, soit Γ un groupe discret et ϱ1, ϱ2 deux representations de Γ dans Sp(2n,ℝ). On suppose que les cocycles ϱ
 1
 *
 σ et ϱ
 2
 *
 σ definissent la meme classe bornee. Que peut-on en conclure sur ϱ1 et ϱ2? Par ailleurs, l'article [At l] traite aussi d'invariants sur SL(2,ℤ) differents de ceux que nous avons consideres, comme par exemple les fonctionsL de Shimizu. Est-il possible de les faire rentrer naturellement dans notre cadre?

Cocycles d'Euler et de Maslov

A selection of aspects of the theory of bounded cohomology is presented. The emphasis
is on questions motivating the use of that theory as well as on some concrete issues suggested
by its study. Specific topics include rigidity, bounds on characteristic classes, quasification, orbit
equivalence, amenability.

/pdf/an-invitation-to-bounded-cohomology-12w5fwwcqf.pdf

An invitation to bounded cohomology

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant

/pdf/maximal-surface-group-representations-in-isometry-groups-of-4tsyom124n.pdf

Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Let D be bounded symmetric domain of rank p, and let o9 be the KRhler form of its Bergmann metric, where the metric is normalized so that the minimum holomorphic sectional curvature is 1. I fX is a compact manifold whose universal cover is D, to defines a cohomology class [to] e H 2 (X, R). The purpose of this paper is to compute its sup norm in the sense of Gromov [5]. We show II [ to] II co = pn. Strictly speaking, we only prove this for three of the four classes of classical domains (cf. Sect. 2). This theorem has the following topological corollary. Let S be a Riemann surface of genus 0 > 1 and f : S ~ X a continuous map. Then ! f ' t o < 4 p ( # 1)n.

The gromov norm of the Kaehler class of symmetric domains

Design synthesis in VLSI and software engineering

Publisher Summary The automation of the diverse tasks in the design, manufacturing, and testing of integrated digital circuits continues to receive great attention. As progress in semiconductor technology made it possible to manufacture integrated circuits (ICs) containing many active devices, automatic tools that help designers in the different stages of the production of circuits became indispensable, creating an entire field of activities referred to today as design automation. The degree of sophistication of automatic tools has evolved accordingly; however, their capabilities have hardly been able to keep pace with the great complexity of the ICs. This chapter discusses systems reported in the literature as being in operation or development and it outlines the nature of silicon compilation and some of its benefits and problems. It discusses the process of silicon compilation, describing the main components of a compiler and different degrees of synthesis and automation. The chapter discusses some areas in which advances may be incorporated into future compilers.

Antun Domic

Papers

The gromov norm of the Kaehler class of symmetric domains

Design synthesis in VLSI and software engineering

Silicon Compilers For VLSI