A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The study proves fixed-point theorems for groups acting on CAT(0) spaces.
Paper extends Brouwer Fixed Point Theorem with amiable and almost amiable fixed sets.
A homological selection theorem for C-spaces, as well as, a finite-dimensional homological selection theorem is established. We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically UV^n set-valued maps.
Banach's fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the natural metric in their domain, making the applicability of Banach's theorem li…
Extends Brouwer fixed point theorem with new conditions for continuous maps.
We prove three theorems giving fixed points for orientation preserving homeomorphisms of the plane following forgotten results of Brouwer.
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
Suppose one is given a discrete group G, a cocompact proper G-manifold M, and a G-self-map f of M. Then we introduce the equivariant Lefschetz class of f, which is globally defined in terms of cellular chain complexes, and the local equivariant Lefschetz class of f, which is locally defined in terms of fixed point data…
In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept of half-continuity coupled with the introduction of local supersolutions. These…
We investigate the fixed point property of the group actions on a coarse space and its Higson corona. We deduce the coarse version of Brouwer's fixed point theorem.
Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of special lagrangian and lagrangian varieties in certain homogeneous spaces.
Paper proves new method for constructing initial data in general relativity.
The paper classifies involutions on S^4, proving linearities under certain conditions.
The fixed-point index of a homeomorphism of Jordan curves measures the number of fixed-points, with multiplicity, of the extension of the homeomorphism to the full Jordan domains in question. The now-classical Circle Index Lemma says that the fixed-point index of a positive-orientation-preserving homeomorphism of round…
The main result in this paper is a fixed point formula for equivariant indices of elliptic differential operators, for proper actions by connected semisimple Lie groups on possibly noncompact manifolds, with compact quotients. For compact groups and manifolds, this reduces to the Atiyah-Segal-Singer fixed point formula…
A fixed point theorem is proved for inverse transducers, leading to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is uniformly continuous for the hyperbolic metric, it is proved that the set of regula…
We prove a global fixed point theorem for the centralizer of a homeomorphism of the two dimensional disk that has attractor-repeller dynamics on the boundary with at least two attractors and two repellers. As one application, we show that there is a finite index subgroup of the centralizer of a pseudo-Anosov homeom…
We develop a new approach to the pulling back fixed point theorem of W. Browder and use it in order to prove various generalizations of this result.
M Handel has proved in [Topology 38 (1999) 235--264] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that may be extended to the closed disk and that satisfies a linking property of orbits. We give here a new proof of Handel's fixed point theorem, based on Brouwer theory and som…
Gromov showed that for fixed, arbitrarily large C, any uniformly C-Lipschitz affine action of a random group in his graph model on a Hilbert space has a fixed point. We announce a theorem stating that more general affine actions of the same random group on a Hilbert space have a fixed point. We discuss some aspects of …
We generalise the Atiyah-Segal-Singer fixed point theorem to noncompact manifolds. Using -theory, we extend the equivariant index to the noncompact setting, and obtain a fixed point formula for it. The fixed point formula is the explicit cohomological expression from Atiyah-Segal-Singer's result. In the noncompact …
The Brouwer fixed point theorem says that any continuous function from disc to itself has a fixed point. By using simple geometrical technique we have generalized the result in manifold and proved that any continuous function on the boundary of a bounded convex domain of a -dimensional Riemannian manifold with a pol…
Fixed points found in cluster modular groups under specific conditions.
Paper finds efficient algorithms for computing fixed points in financial networks.
In this paper we give a natural condition for when a volumorphism on a Riemannian manifold is actually an isometry with respect to some other, optimal, Riemannian metric . We consider the natural action of volumorphisms on the space $\M_μ^s$ of all Riemannian metrics of Sobolev class , , with a f…
In this paper we show that the Seiberg--Witten invariant is zero for all smooth 4--manifolds with which admit circle actions that have at least one fixed point. Furthermore, we show that all symplectic 4--manifolds which admit circle actions with fixed points are rational or ruled, and thus admit a symplectic…
The paper proves a theorem about fixed points and relates it to the Nielsen realisation problem.
New proofs in fixed point theory for manifolds and domains.
The purpose of this mostly expository paper is to discuss a connection between Nielsen fixed point theory and symplectic Floer homology theory for symplectomorphisms of surface and a calculation of Seidel's symplectic Floer homology for different mapping classes. We also describe symplectic zeta functions and asympltot…
Formula for fixed points on noncompact spaces.
We present proofs of basic results, including those developed by Harold Bell, for the plane fixed point problem: does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by Bell but without accessible proofs. We define the concept of the variation of a…
This article generalizes the work of Ballmann and Światkowski to the case of Reflexive Banach spaces and uniformly convex Busemann spaces, thus giving a new fixed point criterion for groups acting on simplicial complexes.
The purpose of this expository paper is to present new directions in the classical Nielsen-Reidemeister fixed point theory. We describe twisted Burnside-Frobenius theorem, groups with \emph{property} and a connection between Nielsen fixed point theory and symplectic Floer homology.
The Grove-Searle theorem on 2d manifolds with 8 or less symmetry groups has positive Euler characteristic.
Characterizes the Legendre involution on generic frontals.
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold . We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the distance function to a closed subset of ; 2) solvability and implicit func…
Given a closed, oriented surface, possibly with boundary, and a mapping class, we obtain sharp lower bounds on the number of fixed points of a surface symplectomorphism (i.e. area-preserving map) in the given mapping class, both with and without nondegeneracy assumptions on the fixed points. This generalizes the Poinca…
Recent proofs of classical theorems in polynomial algebra and functional analysis are discussed, which use tools from the topology of real manifolds. Simpler proofs were discovered in the new century, of the Hilbert Nullstellensatz, and the Gelfand-Mazur Theorem. We give a related proof that an irreducible real polynom…
Walraswap solves batch auction pricing by finding optimal AMM swaps.
Global fixed points in low-dimensional surface group space correspond to trivial representations.
Study of loop braid groups for 3D manifolds, linking algebra and dynamics.
The proof of Brouwer's fixed-point theorem based on Sperner's lemma is often presented as an elementary combinatorial alternative to advanced proofs based on algebraic topology. The goal of this note is to show that: (i) the combinatorial proof of Sperner's Lemma can be considered as a cochain-level version, written in…
In this paper, we first prove a local family version of the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, then we extend the famous Witten's rigidity Theorems to the family case. Several family vanishing theorems for elliptic genera are also proved.
We announce the following result and give several applications: A Hamiltonian -space (for a torus) with isolated fixed points is cobordant to a disjoint union of weighted projective spaces which are constructed from its fixed point data. The applications concern the Duistermaat-Heckman formula, the topological J…
A recent anomaly computation of Horava and Witten is proved and generalized in the form of two index theorems in odd dimensions. Theorem A is a fixed point formula for orientation-reversing involutions. Theorem B is an index theorem for manifolds with boundary using local boundary conditions. Both hold for families of …
Extends G-signature theorem to Witt G-pseudomanifolds.
Study solves optimal portfolio selection using HJB equation.
Paper generalizes Hardy-Rogers maps for market equilibrium analysis in duopoly markets.