We reinvestigate the theory of deformations of tilings using P -equivariant cohomology. In particular we relate the notion of asymptotically negligible shape functions introduced by Clark and Sadun to weakly P -equivariant forms. We then investigate more closely the relation between deformations of patterns and homeomorphism or topological conjugacy of pattern spaces.

We develop a general method to evaluate exactly certain phase space path integrals. Our method is applicable to hamiltonians which are functions of a classical phase space observable that determines the action of a circle on the phase space. Our approach is based on the localization technique, originally introduced to derive the Duistermaat-Heckman integration formula and its path integral gene...

We study the Morse theory of the Yang-Mills-Higgs functional on the space of pairs (A,Φ), where A is a unitary connection on a rank 2 hermitian vector bundle over a compact Riemann surface, and Φ is a holomorphic section of (E, d′′ A). We prove that a certain explicitly defined substratification of the Morse stratification is perfect in the sense of G-equivariant cohomology, where G denotes the...

We determine the possible cohomology algebra of orbit space of any free involution on a mod-2 cohomology lens space X using the Leray spectral sequence associated to the Borel fibration X →֒ XZ2 −→ BZ2 . As an application we show that if X is a mod-2 cohomology lens space of dimension 2m − 1 where 4 ∤ m, then there does not exist any Z2-equivariant map S n → X for n ≥ 2, where S is equipped with...

Abstract. In 1998, Goresky, Kottwitz, and MacPherson showed that for certain projective varieties X equipped with an algebraic action of a complex torus T , the equivariant cohomology ring H∗ T (X) can be described by combinatorial data obtained from its orbit decomposition. In this paper, we generalize their theorem in three different ways. First, our group G need not be a torus. Second, our s...

We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply these inequalities to study cohomology of the fixed points set of a symplectic torus action. We show that in this case our inequalities are perfect, i.e. the...

The purpose of this paper is to explore the relationship between the cyclic homology and cohomology theories of Connes [9-11], see also Loday and Quillen [20], and "IF equivariant homology and cohomology theories. Here II" is the circle group. The most general results involve the definitions of the cyclic homology of cyclic chain complexes and the notions of cyclic and cocyclic spaces so precis...

We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological algebras introduced in a previous paper [35], based on Quillen superconnections and heat-kernel regularization. Then we adapt the formalism to the cyclic coh...

In this article, we introduce equivariant formal deformation theory of Lie triple systems. We an cohomology systems and using study the

We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply these inequalities to study cohomology of the fixed points set of a symplectic torus action. We show that in this case our inequalities are perfect, i.e. the...