Related papers: Restricting cohomology classes to disk and segment…

Understanding the topology of decision regions is central to explaining the inner workings of deep neural networks. Prior empirical work has provided evidence that these regions are path connected. We study a stronger topological question:…

Refinements of the Yang-Mills stratifications of spaces of connections over a compact Riemann surface are investigated. The motivation for this study was the search for a complete set of relations between the standard generators for the…

We consider moduli spaces of $d$-dimensional manifolds with embedded particles and discs. In this moduli space, the location of the particles and discs is constrained by the $d$-dimensional manifold. We will compare this moduli space with…

Let f: S'--> S be a finite and faithfully flat morphism of locally noetherian schemes of constant rank n > 1 and let G be a smooth, commutative and quasi-projective S-group scheme with connected fibers. Under certain restrictions on f and…

Locally convex curves in the sphere $S^n$ have been studied for several reasons, including the study of linear ordinary differential equations. Taking Frenet frames obtains corresponding curves $\Gamma$ in the group $Spin_{n+1}$; $\Pi:…

We study the cohomology ring of the configuration space of unordered points in the two dimensional torus. In particular, we compute the mixed Hodge structure on the cohomology, the action of the mapping class group, the structure of the…

Let $\{V_{i}\}_{i=1}^{n}$ be a finite family of closed subsets of a plane or a sphere $S^{2}$, each homeomorphic to the two-dimensional disk. In this paper we discuss the question how the boundary of connected components of a complement…

In order to look for a well-behaved counterpart to Dolbeault cohomology in D-complex geometry, we study the de Rham cohomology of an almost D-complex manifold and its subgroups made up of the classes admitting invariant, respectively…

Let $\mathcal{M}$ be a differential module, whose coefficients are analytic elements on an open annulus $I$ ($\subset \bR_{>0}$) in a valued field, complete and algebraically closed of inequal characteristic, and let $R(\mathcal{M}, r)$ be…

We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold $\sigma$, we associate an integer-valued function, called degree, measuring the extent to which $\sigma$ fails to be cylindrical. In particular,…

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to B Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc by the identity. By a classical result of Farrell and…

We study graph complexes related to configuration spaces and diffeomorphism groups of highly connected manifolds of odd dimension. In particular we compute the cohomology in the "high genus" limit. This paper is a continuation of previous…

We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K $\in$ R on the regular set, the cone angle along the stratum of codimension two is…

We examine the geometry of loop spaces in derived algebraic geometry and extend in several directions the well known connection between rotation of loops and the de Rham differential. Our main result, a categorification of the geometric…

We consider rotationally symmetric $p$-harmonic maps from the unit disk $D^2\subset\real^2$ to the unit sphere $S^2\subset\real^3$, subject to Dirichlet boundary conditions and with $1<p<\infty$. We show that the associated energy…

An $n$-dimensional ($n\geq 2$) simply connected, compact without boundary Finsler space of positive constant sectional curvature is conformally homeomorphic to an n-sphere in the Euclidean space $\R^{n+1}$.

A building block of noncommutative geometry is the observation that most of the geometric information of a compact riemannian spin manifold M is encoded within its Dirac operator D. Especially via Connes' distance formula one is able to…

We construct families of differential graded algebras R and R \boxtimes R and give an algebraic formulation of the contact category of a disk through the differential graded category DGP(R) generated by some distinguished projective…

We give a recursive algorithm for computing the Orlik-Terao algebra of the Coxeter arrangement of type A_{n-1} as a graded representation of S_n, and we give a conjectural description of this representation in terms of the cohomology of the…

A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup D of G that acts properly discontinuously on G/H, such that the quotient space D\G/H is compact. When n is even, we find every closed,…