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1.
Metrics of constant negative curvature on a compact Riemann surface are critical points of the Liouville action functional, which in recent constructions is rigorously defined as a class in a ech-de Rham complex with respect to a suitable covering of the surface. We show that this class is the square of the metrized holomorphic tangent bundle in hermitian-holomorphic Deligne cohomology. We achieve this by introducing a different version of the hermitian-holomorphic Deligne complex which is nevertheless quasi-isomorphic to the one introduced by Brylinski in his construction of Quillen line bundles. We reprove the relation with the determinant of cohomology construction. Furthermore, if we specialize the covering to the one provided by a Kleinian uniformization (thereby allowing possibly disconnected surfaces) the same class can be reinterpreted as the transgression of the regulator class expressed by the Bloch-Wigner dilogarithm. 相似文献
2.
C.P. Walkden 《Communications in Mathematical Physics》1999,205(2):263-281
We consider a hyperbolic flow φ
t
defined on an attracting basic set Λ. A map from the first (Čech) cohomology group of Λ into the dynamic cohomology group
is constructed. This map is used to discuss the stable ergodicity and mixing of compact Lie group extensions and velocity
changes of φ
t
.
Received: 17 June 1998 / Accepted: 24 February 1999 相似文献
3.
We formulate and solve the analog of the universal Conformal Ward Identity for the stress-energy tensor on a compact Riemann
surface of genus g > 1, and present a rigorous invariant formulation of the chiral sector in the induced two-dimensional gravity on higher genus
Riemann surfaces. Our construction of the action functional uses various double complexes naturally associated with a Riemann
surface, with computations that are quite similar to descent calculations in BRST cohomology theory. We also provide an interpretation
of the action functional in terms of the geometry of different fiber spaces over the Teichmüller space of compact Riemann
surfaces of genus g > 1.
Received: 12 September 1996 / Accepted: 6 January 1997 相似文献
4.
Ha?ja Moustafa 《Communications in Mathematical Physics》2010,298(2):369-405
In this paper, we first remind how we can see the “hull” of the pinwheel tiling as an inverse limit of simplicial complexes
(Anderson and Putnam in Ergod Th Dynam Sys 18:509–537, 1998) and we then adapt the PV cohomology introduced in Savinien and
Bellissard (Ergod Th Dynam Sys 29:997–1031, 2009) to define it for pinwheel tilings. We then prove that this cohomology is
isomorphic to the integer Čech cohomology of the quotient of the hull by S
1 which let us prove that the top integer Čech cohomology of the hull is in fact the integer group of coinvariants of the canonical
transversal Ξ of the hull. The gap-labeling for pinwheel tilings is then proved and we end this article by an explicit computation
of this gap-labeling, showing that
mt ( C(X,\mathbb Z) ) = \frac1264\mathbb Z [ \frac15]{\mu^t \left( C(\Xi,\mathbb {Z}) \right) = \frac{1}{264}\mathbb {Z} \left [ \frac{1}{5}\right ]}. 相似文献
5.
The Dirac q-monopole connection is used to compute projector matrices of quantum Hopf line bundles for arbitrary winding number. The
Chern–Connes pairing of cyclic cohomology and K-theory is computed for the winding number −1. The non-triviality of this pairing is used to conclude that the quantum principal
Hopf fibration is non-cleft. Among general results, we provide a left-right symmetric characterization of the canonical strong
connections on quantum principal homogeneous spaces with an injective antipode. We also provide for arbitrary strong connections
on algebraic quantum principal bundles (Hopf–Galois extensions) their associated covariant derivatives on projective modules.
Received: Received: 4 September 1998 / Accepted: 16 October 1998 相似文献
6.
《Journal of Geometry and Physics》1999,29(4):347-392
These notes grew out of the Quantisation Seminar 1997–1998 on Deligne's paper [P. Deligne, Déformations de l'algèbre des fonctions d'une variété symplectique: Comparison entre Fedosov et De Wilde, Lecomte, Selecta Math. (New Series) 1 (1995) 667–697] and the lecture of the first author in the Workshop on Quantisation and Momentum Maps at the University of Warwich in December 1997.We recall the definitions of the cohomology classes introduced by Deligne for equivalence classes of differential star products on a symplectic manfold and show the properties of the relations between these classes by elementary methods based on Čech cohomology. 相似文献
7.
These notes grew out of the Quantisation Seminar 1997–1998 on Deligne's paper [P. Deligne, Déformations de l'algèbre des fonctions d'une variété symplectique: Comparison entre Fedosov et De Wilde, Lecomte, Selecta Math. (New Series) 1 (1995) 667–697] and the lecture of the first author in the Workshop on Quantisation and Momentum Maps at the University of Warwich in December 1997.We recall the definitions of the cohomology classes introduced by Deligne for equivalence classes of differential star products on a symplectic manfold and show the properties of the relations between these classes by elementary methods based on
ech cohomology. 相似文献
8.
We construct projective unitary representations of the smooth Deligne cohomology group of a compact oriented Riemannian manifold of dimension 4k+1, generalizing positive energy representations of the loop group of the circle at level 2. We also classify such representations under a certain condition. The number of the equivalence classes of irreducible representations being finite is determined by the cohomology of the manifold. 相似文献
9.
T. Perutz 《Communications in Mathematical Physics》2008,278(2):289-306
The n
th symmetric product of a Riemann surface carries a natural family of K?hler forms, arising from its interpretation as a moduli
space of abelian vortices. We give a new proof of a formula of Manton–Nasir [10] for the cohomology classes of these forms.
Further, we show how these ideas generalise to families of Riemann surfaces.
These results help to clarify a conjecture of D. Salamon [13] on the relationship between Seiberg–Witten theory on 3–manifolds
fibred over the circle and symplectic Floer homology. 相似文献
10.
We reformulate the concept of connection on a Hopf–Galois extension B⊆P in order to apply it in computing the Chern–Connes pairing between the cyclic cohomology HC
2
n
(B) and K
0 (B). This reformulation allows us to show that a Hopf–Galois extension admitting a strong connection is projective and left
faithfully flat. It also enables us to conclude that a strong connection is a Cuntz–Quillen-type bimodule connection. To exemplify
the theory, we construct a strong connection (super Dirac monopole) to find out the Chern–Connes pairing for the super line
bundles associated to a super Hopf fibration.
Received: 8 March 2000 / Accepted: 5 January 2001 相似文献
11.
Interpreting the number of ramified covering of a Riemann surface by Riemann surfaces as the relative Gromov–Witten invariants
and applying a gluing formula, we derive a recursive formula for the number of ramified covering of a Riemann surface by Riemann
surface with elementary branch points and prescribed ramification type over a special point.
Received: 10 June 1999 / Accepted: 7 July 2000 相似文献
12.
We study a quantum version of the SU(2) Hopf fibration and its associated twistor geometry. Our quantum sphere arises as the unit sphere inside a q-deformed quaternion space . The resulting four-sphere is a quantum analogue of the quaternionic projective space . The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space and use it to study a system of anti-self-duality equations on , for which we find an ‘instanton’ solution coming from the natural projection defining the tautological bundle over . 相似文献
13.
《Journal of Geometry and Physics》2006,56(9):1534-1560
In this paper we compute explicit formulas for the holonomy map for a gerbe with connection over an orbifold. We show that the holonomy descends to a transgression map in Deligne cohomology. We prove that this recovers both the inner local systems in Ruan’s theory of twisted orbifold cohomology [1] and the local system of Freed–Hopkins–Teleman in their work in twisted K-theory [2]. In the case in which the orbifold is simply a manifold we recover previous results of Gawȩdzki [3] and Brylinski[4]. 相似文献
14.
Friedrich Wagemann 《Communications in Mathematical Physics》1999,208(2):521-540
This article continues work of B. L. Feigin [5] and N. Kawazumi [15] on the Gelfand-Fuks cohomology of the Lie algebra of
holomorphic vector fields on a complex manifold. As this is not always an interesting Lie algebra (for example, it is 0 for
a compact Riemann surface of genus greater than 1), one looks for other objects having locally the same cohomology. The answer
is a cosimplicial Lie algebra and a differential graded Lie algebra (well known in Kodaira–Spencer deformation theory). We
calculate the corresponding cohomologies and the result is very similar to the result of A. Haefliger [12], R. Bott and G.
Segal [2] in the case of vector fields. Applications are in conformal field theory (for Riemann surfaces), deformation theory and foliation theory.
Received: 25 February 1999 / Accepted: 20 July 1999 相似文献
15.
We calculate a second cohomology class which determines a deformation quantization up to equivalence for a deformation quantization with separation of variables on a Kähler manifold, following P. Deligne. 相似文献
16.
A. K. Raina 《Letters in Mathematical Physics》1990,19(1):1-5
We prove that the correlation functions of a system of chiral fermions on a compact Riemann surface are determined by postulating their behaviour at coincident points and a principle of maximal analyticity. The proof proceeds by a reformulation as a problem of sheaf cohomology. Wick's theorem and the Fay identities are rigorous consequences of our analysis. 相似文献
17.
We use previous work on the chiral de Rham complex and Borisov's deformation of a lattice vertex algebra to give a simple
linear algebra construction of quantum cohomology of toric varieties. Somewhat unexpectedly, the same technique allows to
compute the formal character of the cohomology of the chiral de Rham complex on even dimensional projective spaces. In particular,
we prove that the formal character of the space of global sections equals the equivariant signature of the loop space, a well-known
example of the Ochanine-Witten elliptic genus.
Received: 15 July 2000 / Accepted: 17 August 2002 Published online: 8 January 2003
RID="*"
ID="*" Partially supported by an NSF grant
Communicated by R. H. Dijkgraaf 相似文献
18.
We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A–model). The second theory is an intermediate model, which we call the I–model. The equivalence between the A–model and the I–model is achieved by realizing the former as a deformation of a linear sigma model with a complex torus as the target and then applying to it a version of the T–duality. On the other hand, the I–model is closely related to the twisted Landau-Ginzburg model (the B–model) that is mirror dual to the A–model. Thus, the mirror symmetry is realized in two steps, via the I–model. In particular, we obtain a natural interpretation of the superpotential of the Landau-Ginzburg model as the sum of terms corresponding to the components of a divisor in the toric variety. We also relate the cohomology of the supercharges of the I–model to the chiral de Rham complex and the quantum cohomology of the underlying toric variety.Partially supported by the DARPA grant HR0011-04-1-0031 and the NSF grant DMS-0303529.Partially supported by the Federal Program 40.052.1.1.1112, by the Grants INTAS 03-51-6346, NSh-1999/2003.2 and RFFI-04-01- 00637. 相似文献
19.
We calculate the continuous cohomology of the Lie algebra of meromorphic vector fields on a compact Riemann surface from the cohomology of the holomorphic vector fields on the open Riemann surface pointed in the poles. This cohomology has been given by Kawazumi. Our result shows the Feigin–Novikov conjecture. 相似文献
20.
The relation between superholomorphicity and holomorphicity of chiral superstring N-point amplitudes for NS bosons on a genus 2 Riemann surface is shown to be encoded in a hybrid cohomology theory, incorporating elements of both de Rham and Dolbeault cohomologies. A constructive algorithm is provided which shows that, for arbitrary N and for each fixed even spin structure, the hybrid cohomology classes of the chiral amplitudes of the N-point function on a surface of genus 2 always admit a holomorphic representative. Three key ingredients in the derivation are a classification of all kinematic invariants for the N-point function, a new type of 3-point Green's function, and a recursive construction by monodromies of certain sections of vector bundles over the moduli space of Riemann surfaces, holomorphic in all but exactly one or two insertion points. 相似文献