All posts under category "Mathematics / Math.GT"
We prove that the space $M(K(x,y))$ of $mathbb R$-places of the field $K(x,y)$ of rational functions of two variables with coefficients in a totally Archimedean field $K$ has covering and integral dimensions $dim M(K(x,y))=dim_IZ M(K(x,y))=2$ and the cohomological dimension $dim_G M(K(x,y))=1$ for a
In this thesis, we consider semi-algebraic sets over a real closed field $R$ defined by quadratic polynomials. Semi-algebraic sets of $R^k$ are defined as the smallest family of sets in $R^k$ that contains the algebraic sets as well as the sets defined by polynomial inequalities, and which is also c
This paper studies compactifications of moduli spaces involving closed Riemann surfaces. The first main result identifies the homeomorphism types of these compactifications. The second main result introduces orbicell decompositions on these spaces using semistable ribbon graphs extending the earlier
The main aim of this paper is the construction of a smooth (sometimes called differential) extension hat{MU} of the cohomology theory complex cobordism MU, using cycles for hat{MU}(M) which are essentially proper maps Wto M with a fixed U(n)-structure and U(n)-connection on the (stable) normal bundl
We show that for every positive integer n there is a simple closed curve in the plane (which can be taken infinitely differentiable and convex) which has exactly n inscribed squares.
A triangulation of a surface is called $q$-equivelar if each of its vertices is incident with exactly $q$ triangles. In 1972 Altshuler had shown that an equivelar triangulation of torus has a Hamiltonian Circuit. Here we present a necessary and sufficient condition for existence of a contractible Ha
We show that a weighted homogeneous complex surface singularity is metrically conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest weights are equal. We also give an example of a pair of weighted homogeneous complex surface singularities that are topologically equivalent b
Starting from ideas of Furuta, we develop a general formalism for the construction of cohomotopy invariants associated with a certain class of $S^1$-equivariant non-linear maps between Hilbert bundles. Applied to the Seiberg-Witten map, this formalism yields a new class of cohomotopy Seiberg-Witten
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 o
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
Motivated by the $y$-ification of HOMFLY--PT homology by Gorsky and Hogancamp, and the $mathfrak{sl}_2$-action of Gorsky, Hogancamp, and Mellit, we construct $y$-ifications of Khovanov homology and its equivariant versions within Bar-Natan's framework for tangles, and define an action of the element
Conjecture 1 of Stanley Chang: 'Positive scalar curvature of totally nonspin manifolds' asserts that a closed smooth manifold M with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain homological condition is satisfied. We present a counterexample to th
Given a multifunction from $X$ to the $k-$fold symmetric product $Sym_k(X)$, we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally mul
In this paper, we consider the action of the Goeritz group $mathcal G_p$ for the genus two Heegaard splitting of the lens space $L(p,1)$ with $pge 2$ on the homology of the Heegaard surface. We describe the action in terms of matrices in $GL(4, mathbb Z)$, and provide homology and homotopy obstructi
We classify Riemannian foliations of manifolds homeomorphic to CROSSes.
We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.
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