Related papers: On topological classification of complex mappings
Parametrized motion planning algorithms have high degree of flexibility and universality, they can work under a variety of external conditions, which are viewed as parameters and form part of the input of the algorithm. In this paper we…
We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal crossing number of embedded…
Given a compact Riemannian manifold with boundary, we prove that the space of embedded, which may be improper, free boundary minimal hypersurfaces with uniform area and Morse index upper bound is compact in the sense of smoothly graphical…
We present new invariant machine learning models that approximate the Ricci-flat metric on Calabi-Yau (CY) manifolds with discrete symmetries. We accomplish this by combining the $\phi$-model of the cymetric package with non-trainable,…
We characterize the Zariski topologies over an algebraically closed field in terms of general dimension-theoretic properties. Some applications are given to complex manifold and to strongly minimal sets.
As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…
In low dimensional topology, we have some invariants defined by using solutions of some nonlinear elliptic operators. The invariants could be understood as Euler class or degree in the ordinary cohomology, in infinite dimensional setting.…
For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the…
We compute the topological mapping class group of every compact, simply connected, topological 4-manifold. This was previously only known in the closed case. If the 4-manifold is smooth, we deduce an analogous description of the stable…
Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the…
We show that for a smooth, closed 2-connected manifold $M$ of dimension $d \geq 6$, the topological mapping class group $\pi_0 \mathrm{Homeo}(M)$ is residually finite, in contrast to the situation for the smooth mapping class group $\pi_0…
Given a positive integer $p$, we consider $W^{1,p}$-maps from a Euclidean domain of dimension $p+1$ into a closed Riemannian manifold $\mathcal{N}$. The target manifold is required to satisfy suitable topological conditions; in particular,…
Suppose $\phi$ is a $\mathbb{Z}/4$-cover of a curve over an algebraically closed field $k$ of characteristic $2$, and $\Phi_1$ is a \emph{nice} lift of $\phi$'s $\mathbb{Z}/2$-sub-cover to a complete discrete valuation ring $R$ in…
The 2d O(3) model is widely used as a toy model for ferromagnetism and for Quantum Chromodynamics. With the latter it shares --- among other basic aspects --- the property that the continuum functional integral splits into topological…
We study the query complexity of finding a Tarski fixed point over the $k$-dimensional grid $\{1,\ldots,n\}^k$. Improving on the previous best upper bound of $\smash{O(\log^{\lceil 2k/3\rceil} n)}$ [FPS20], we give a new algorithm with…
Suppose $\phi$ is a wildly ramified cover of germs of curves defined over an algebraically closed field of characteristic p. We study unobstructed deformations of $\phi$ in equal characteristic, which are equiramified in that the branch…
We show that the spaces of holomorphic and continuous maps from a smooth complex projective variety to a projective space have the same homology in a range depending on the degree of the maps.
We revisit the classical constructions of tensor-triangular geometry in the setting of stably symmetric monoidal idempotent-complete $\infty$-categories, henceforth referred to as 2-rings. In this setting, we produce a Zariski topology, a…
Iterated Segre mappings of real analytic generic submanifolds in complex space have been an essential tool in the study of holomorphic, formal, and CR mappings between such manifolds. In this paper we present a theory of iterated Segre…
Without leaving finite mathematics and using finite topological spaces only, we give a definition of homeomorphisms of finite abstract simplicial complexes or finite graphs. Besides exploring the definition in various contexts, we add some…