Related papers: Generalized plumbings and Murasugi sums

Following some recent work by Gross, we consider the partition function for QCD on a two dimensional torus and study its stringiness. We present strong evidence that the free energy corresponds to a sum over branched surfaces with small…

We generalize a compactification technique due to C. Simpson in the context of $\mathbb{G}_m$-actions over the ground field of complex numbers, to the case of a universally Japanese base ring. We complement this generalized compactification…

We give elementary constructions of manifold with corner structures and associative gluing maps on compactifications of spaces of infinite, half infinite, and finite Morse flow lines.

We prove that if a closed manifold $B$ is a connected component of the binding of an open book decomposition of a manifold $M$, then every open book decomposition of $B$ spun embeds in $M$. As an application, we prove that every open book…

Graph manifolds form important classes of $3$-dimensional closed and orientable manifolds. For example, {\it Seifert} manifolds are graph manifolds where hyperbolic manifolds are not. In applying singularity theory of differentiable maps to…

The moduli space of flat SU(2) connections on a punctured surface, having prescribed holonomy around the punctures, is a compact smooth manifold if the prescription is generic. This paper gives a direct, elementary proof that the trace of…

In this paper, as a fundamental study on the theory of Morse functions and their higher dimensional versions or fold maps and applications to geometric theory of manifolds, which were started in 1950s by differential topologists such as…

We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group…

Triangular map is a recent construct in probability theory that allows one to transform any source probability density function to any target density function. Based on triangular maps, we propose a general framework for high-dimensional…

We develop a global theory for complete hypersurfaces in $\mathbb{R}^{n+1}$ whose mean curvature is given as a prescribed function of its Gauss map. This theory extends the usual one of constant mean curvature hypersurfaces in…

In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…

The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…

Let $\Omega_1,\Omega_2$ be two disjoint open sets in $\mathbf C^n$ whose boundaries share a smooth real hypersurface $M$ as relatively open subsets. Assume that $\Omega_i$ is equipped with a complex structure $J^i$ which is smooth up to…

We observe that the classical Borsuk-Ulam theorem has an easy generalization to maps from an n-manifold M^n to R^n. We point out a geometric corollary.

For $m=2$ and $m=3$ we prove that any connected, oriented, open manifold $M^m$ admits a simple branched covering map over $\mathbb{R}^m$. When $M$ has $k$ ends and $k$ is finite, the degree of the cover can be taken to be $mk$. Regardless…

We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…

A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…

This paper introduces and studies a categorical analogue of the familiar monoid semiring construction. By introducing an axiomatisation of summation that unifies notions of summation from algebraic program semantics with various notions of…

We show that every topological surface lamination of a 3-manifold M is isotopic to one with smoothly immersed leaves. This carries out a project proposed by Gabai in [Problems in foliations and laminations, AMS/IP Stud. Adv. Math. 2.2…