Higgs bundles and surface group representations in the real symplectic group

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Higgs Bundles and Surface Group Representations in the Real Symplectic Group

In this paper we study the moduli space of representations of a surface group (i.e., the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n,R). The moduli space is partitioned by an integer invariant, called the Toledo invariant. This invariant is bounded by a Milnor–Wood type inequality. Our main result is a count of the number of connected components of the mod...

متن کامل

Surface group representations to SL(2,C) and Higgs bundles with smooth spectral data

Let Σ be a closed, oriented surface of genus g ≥ 2. In this short note we answer a special case of the following question posed by Nigel Hitchin: which representations ρ : π1(Σ) → SL(n,C) correspond to Higgs bundles which lie outside the discriminant locus of the Hitchin fibration for some Riemann surface structure on Σ? For example, the Higgs field for a unitary representation (i.e. one whose ...

متن کامل

Symplectic torus bundles and group extensions

Symplectic torus bundles ξ : T 2 → E → B are classified by the second cohomology group of B with local coefficients H1(T ). For B a compact, orientable surface, the main theorem of this paper gives a necessary and sufficient condition on the cohomology class corresponding to ξ for E to admit a symplectic structure compatible with the symplectic bundle structure of ξ : namely, that it be a torsi...

متن کامل

Group Quasi-representations and Almost Flat Bundles

We study the existence of quasi-representations of discrete groups G into unitary groups U(n) that induce prescribed partial maps K0(C ∗(G)) → Z on the K-theory of the group C*-algebra of G. We give conditions for a discrete group G under which the K-theory group of the classifying space BG consists entirely of almost flat classes.

متن کامل

Least-Squares on the Real Symplectic Group

The present paper discusses the problem of least-squares over the real symplectic group of matrices Sp(2n,R). The least-squares problem may be extended from flat spaces to curved spaces by the notion of geodesic distance. The resulting non-linear minimization problem on manifold may be tackled by means of a gradient-descent algorithm tailored to the geometry of the space at hand. In turn, gradi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Topology

سال: 2012

ISSN: 1753-8416

DOI: 10.1112/jtopol/jts030