arXiv research

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.

Unified framework recovers and improves classical Brouwer homeomorphism results.

Extends Brouwer fixed point theorem with new conditions for continuous maps.

Continuous functions on Riemannian manifolds with poles have fixed points.

Paper extends Brouwer Fixed Point Theorem with amiable and almost amiable fixed sets.

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.

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…

Walraswap solves batch auction pricing by finding optimal AMM swaps.

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…

We give new tools for homotopy Brouwer theory. In particular, we describe a canonical reducing set (the set of "walls") which splits the plane into maximal translation areas and irreducible areas. We then focus on Brouwer mapping classes relatively to four orbits and describe them explicitly by adding to Handel's diagr…

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…

We answer the question of when a new point can be added in a continuous way to configurations of $n$ distinct points in a closed ball of arbitrary dimension. We show that this is possible given an ordered configuration of $n$ points if and only if $n \neq 1$. On the other hand, when the points are not ordered and the d…

Study Kazdan-Warner equations on graphs using Brouwer degree theory.

Framework for games with uncertain parameters, ensuring no player can improve by changing strategy.

We give an answer to the question given by T.Y.Kong in his article "Can 3-D Digital Topology be Based on Axiomatically Defined Digital Spaces?" In this article he asks the question, if so called "good pairs" of neighborhood relations can be found on the set Z^n such that the existence of digital manifolds of dimension …

Moebius-Kantor graph connects multiple groups and topological properties.

New proof shows no flat embedding for Petersen family graphs.

We prove a discrete Jordan-Brouwer-Schoenflies separation theorem telling that a (d-1)-sphere H embedded in a d-sphere G defines two different connected graphs A,B in G such a way that the intersection of A and B is H and the union is G and such that the complementary graphs A,B are both d-balls. The graph theoretic de…

We consider the energy supercritical wave maps from $\mathbb{R}^d$ into the $d$-sphere $\mathbb{S}^d$ with $d \geq 7$. Under an additional assumption of 1-corotational symmetry, the problem reduces to the one dimensional semilinear wave equation $$\partial_t^2 u = \partial^2_r u + \frac{(d-1)}{r}\partial_r u - \frac{(d…

New tiles in higher dimensions are shown to be homeomorphic to balls.

We prove the following new characterization of $C^p$ (Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space $X$ has a $C^p$ smooth (Lipschitz) bump function if and only if it has another $C^p$ smooth (Lipschitz) bump function $f$ such that $f'(x)\neq 0$ for every point $x$ in the interior of the …

A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer's topological degree for the solution of functional equations. It is shown to be very useful for multiwarped spacetimes, which include different types of relativistic spacetimes.

A new method calculates the minimum volume swept by a sphere's homotopy in 3D space.

We consider the energy supercritical harmonic heat flow from $\mathbb{R}^d$ into the $d$-sphere $\mathbb{S}^d$ with $d \geq 7$. Under an additional assumption of 1-corotational symmetry, the problem reduces to the one dimensional semilinear heat equation $$\partial_t u = \partial^2_r u + \frac{(d-1)}{r}\partial_r u - \…

Paper proves a new criterion for time-like geodesics in flat spacetimes.

This paper defines ribbons and ribbon complexes in CW spaces and analyzes their topological properties.

The paper classifies circle actions on 6D manifolds with isolated fixed points.

Groups with special properties always have fixed points.

Study fixed points in digital images, introducing new invariants.

Fixed-point techniques compute semifree geometric circle-equivariant complex cobordism.

Quantized neural networks can represent all fixed-point functions under certain conditions.

Study circle actions on unitary manifolds with discrete fixed points.

Research shows quadratic growth in derivative maxima for certain interval diffeos with parabolic fixed points.

New proof for 6D symplectic manifold with 4 fixed points.

The paper highlights issues with fixed point claims in digital images.

The paper highlights issues in fixed point claims in digital topology.

In this paper, we study a circle action on a compact oriented manifold with a discrete fixed point set. The fixed point data consists of the weights of the $S^1$-representations at the fixed points. We prove various results and properties of the action, in terms of the fixed point data. We show that the manifold can be…

Study fixed point indices and words at infinity for graph selfmaps.

Improved convergence of fixed-point methods using windowed Anderson acceleration.

The paper introduces fixed-point centralities for networks and graphons.

Critiques incorrect fixed point assertions in digital topology.

Study circle actions on manifolds with 3 fixed points, finding dimension constraints and unique structures.

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…

Paper finds at least 6 fixed points for a specific circle action on a 10D manifold.

Corrects incorrect assertions about fixed points in digital topology.

Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the model. To understand this dependence it is interesting to find \emph{all} fixed poi…

Incorrect fixed point assertions in digital topology are discussed.