2,628 research outputs found
On the existence of approximated equilibria in discontinuous economies.
In this paper, we prove an existence theorem for approximated equilibria in a class of discontinuous economies. The existence result is a direct consequence of a discontinuous extension of Brouwer’s fixed point Theorem (1912), and is a refinement of several classical results in the standard general equilibrium with incomplete markets (GEI) model. [Brouwer, L.E.J., 1912. Über Abbildung von Mannigfaltigkeiten. Mathematische Annalen 71, 97–115.] As a by-product, we get the first existence proof of an approximated equilibrium in the GEI model, without perturbing the asset structure nor the endowments. Our main theorem rests on a new topological structure result for the asset equilibrium space and may be of interest by itself.General equilibrium; Incomplete markets; Discontinuity; Fixed point;
Homogeneous Transformation Groups of the Sphere
In this paper, we study the structure of homogeneous subgroups of the
homeomorphism group of the sphere, which are defined as closed groups of
homeomorphisms of the sphere that contain the rotation group. We prove two
structure theorems about the behaviour and properties of such groups and
present a diagram of the structure of these groups partly on the basis of these
results. In addition, we prove a number of explicit relations between the
groups in the diagram.Comment: This paper has been withdrawn by an irreconcilable difference of
opinion between the authors on its presentation and content
Reduction of the Hall-Paige conjecture to sporadic simple groups
A complete mapping of a group is a permutation such
that is also a permutation. Complete mappings of are
equivalent to tranversals of the Cayley table of , considered as a latin
square. In 1953, Hall and Paige proved that a finite group admits a complete
mapping only if its Sylow-2 subgroup is trivial or non-cyclic. They conjectured
that this condition is also sufficient. We prove that it is sufficient to check
the conjecture for the 26 sporadic simple groups and the Tits group
Period Mappings and Ampleness of the Hodge line bundle
We discuss progress towards a conjectural Hodge theoretic completion of a
period map. The completion is defined, and we conjecture that it admits the
structure of a compact complex analytic variety. The conjecture is proved when
the image of the period map has dimension 1,2. Assuming the conjecture holds,
we then prove that the augmented Hodge line bundle extends to an ample line
bundle on the completion. In particular, the completion is a projective
algebraic variety that compactifies the image, analogous to the
Satake-Baily-Borel compactification.Comment: 62 pages. v2 significant revision of the initial submission (v1); v3
further improvements and new references adde
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