Le but de cet exposé est de relater les liens entre dynamique et géométrie. Les systèmes abordés relèvent de la robotique et nous verrons qu’en ce domaine, la quête de mécanismes de plus en plus sophistiqués, et de leur modèles dynamiques associés, se traduit par la complexification des structures géométriques qu’ils impliquent. Le point de vue adopté est celui du calcul des variations de type ...

Abstract. We study the Z2-equivariant K-theory of M(A), where M(A) is the complement of the complexification of a real hyperplane arrangement, and Z2 acts on M(A) by complex conjugation. We compute the rational equivariant Kand KO-rings of M(A), and we give two different combinatorial descriptions of a subring Line(A) of the integral equivariant KO-ring, where Line(A) is defined to be the subri...

Abstract. We study the Z2-equivariant K-theory of M(A), where M(A) is the complement of the complexification of a real hyperplane arrangement, and Z2 acts on M(A) by complex conjugation. We compute the rational equivariant K and KO rings of M(A), and we give two different combinatorial descriptions of a subring Line(A) of the integral equivariant KO ring, where Line(A) is defined to be the subr...

Also available in a PDF version for printing convenience. Previously distributed under the title: Global Complexification of Classic Hellenic Metaphors: transcending the Euro-centric "pillars" of institutional architecture and strategy. The theme has been further developed in associated papers: Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of...

In this paper, we explore holomorphic Segre preserving maps. First, we investigate holomorphic Segre preserving maps sending the complexificationM of a generic real analytic submanifold M ⊆ C of finite type at some point p into the complexification M′ of a generic real analytic submanifold M ′ ⊆ C ′ , finitely nondegenerate at some point p. We prove that for a fixed M and M , the germs at (p, p̄...

We study one-dimensional QCD at finite quark density by using the sign optimization framework. The fermion problem is mitigated deforming path integral domain, $SU(3)$ to a complexified one ${\cal M} \subset SL(3)$, explicitly constructed reduce phase fluctuations. complexification angular representation of $SU(3)$. provide physical explanation procedure in terms complex saddle points. This pic...

The complex version of Bohr-Sommerfeld conditions is proposed. The BPU-construction (see [BPU] or [T1]) is generalized to this complexification. The new feature of this generalization is a spectral curve. The geometry of such curves is investigated. 1 Global structures on subspaces of Lagrangian cycles Let (M,ω) be a smooth symplectic manifold of dimesion 2n. It can be considered as a phase spa...

We show how the Cauchy (or, more generally, the Leray) residue formula can be understood as an informal complex analog of the Stokes formula. It allows one to treat the Poisson (and symplectic) structures on the moduli spaces of at connections on real manifolds and those structures on the moduli spaces of holomorphic bundles on complex manifolds in a parallel way.

An arrangement L of k pairwise non-parallel lines in the complex hyperbolic plane H(C) has a link at infinity K∞(L) comprising k unknotted circles in S, whose topology reflects the combinatorics of L “at infinity”. Many links at infinity are far from being fibered; but if L = C LR is the complexification of a connected hyperbolic R-line arrangement LR ⊂ H(R), then K∞(L) is fibered. §