A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New 2D complex hyperbolic structures found on sphere orbibundles.
Develops orbibundle theory for complex hyperbolic geometry.
Study complex hyperbolic structures on a disc orbibundle with 5 cone points.
Study on invariants of complex hyperbolic disc bundles over surfaces, proving a conjecture.
In the first part of this article we provide a geometrically oriented approach to the theory of orbispaces which originally had been introduced by Chen. We explain the notion of a vector orbibundle and characterize the good sections of a reduced vector orbibundle as the smooth stratified sections. In the second part of…
Study Higgs bundles and flat connections on quasi-regular Sasakian manifolds.
We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential Topology/Geometry, including orbibundles, differential forms, integration and (equivariant) …
We present the theory of pseudodifferential operators acting on a vector orbibundle over an orbifold, construct the zeta function of an elliptic pseudodifferential operator and show the existence of a meromorphic extension to the complex plane with at most simple poles. We give formulas for generalized densities on the…
For a compact, smooth C^r orbifold (without boundary), we show that the topological structure of the orbifold diffeomorphism group is a Banach manifold for finite r \ge 1 and a Frechet manifold if r=infty. In each case, the local model is the separable Banach (Frechet) space of C^r (C^infty, resp.) orbisections of the …
We examine open books with powers of fibered Dehn twists as monodromy. The resulting contact manifolds can be thought of as Boothby-Wang orbibundles over symplectic orbifolds. Using the mean Euler characteristic of equivariant symplectic homology we can distinguish these contact manifolds and hence show that some fiber…
The paper studies Sasaki-Ricci solitons on Sasakian manifolds up to seven dimensions.
Stein fillability of circle bundles over symplectic manifolds is restricted.
This paper studies both the conductance and charge transport on 2D orbifolds in a strong magnetic field. We consider a family of Landau Hamiltonians on a complex, compact 2D orbifold that are parametrised by the Jacobian torus of . We calculate the degree of the associated stable holomorphic spectral orbi…
Every compact aspherical Riemannian manifold admits a canonical series of orbibundle structures with infrasolv fibers which is called its infrasolv tower. The tower arises from the solvable radicals of isometry group actions on the universal covers. Its length and the geometry of its base measure the degree of continuo…
We present an approach to Gromov-Witten invariants that works on arbitrary (closed) symplectic manifolds. We avoid genericity arguments and take into account singular curves in the very formulation. The method is by first endowing mapping spaces from (prestable) algebraic curves into the symplectic manifold with the st…
The paper shows convergence of Sasaki-Ricci flow on Sasakian 5-manifolds.
Study of lattices and subgroups in PSL2(R) with grafting continuity.
The paper proves the existence of Sasaki-Einstein metrics on specific Sasakian manifolds.
We consider four notions of maps between smooth C^r orbifolds O, P with O compact (without boundary). We show that one of these notions is natural and necessary in order to uniquely define the notion of orbibundle pullback. For the notion of complete orbifold map, we show that the corresponding set of C^r maps between …
New research finds 145 infinite families of CS spheres are standard.
Kervaire's sphere-link is equivalent to a ribbon sphere-link, simplifying complex 2-complexes.
New theory proves infinite homology 3-spheres in homology 4-spheres.
Infinitely many splitting spheres found for unlinked 2-spheres in 4-space.
Reduces weak reducing pairs to spheres in 3-sphere Heegaard surfaces.
The study shows how to construct -spheres from -spheres and -balls without additional vertices.
New proof for sphere recognition algorithm.
Proves stability of convex spheres with similar geodesic lengths.
Soliton spheres are immersed 2-spheres in the conformal 4-sphere S^4=HP^1 that allow rational, conformal parametrizations f:CP^1->HP^1 obtained via twistor projection and dualization from rational curves in CP^{2n+1}. Soliton spheres can be characterized as the case of equality in the quaternionic Pluecker estimate. A …
Study on sphere immersions and their stability indices.
The paper constructs biharmonic maps between spheres using polynomial maps.
Reduces connectivity problem for genus-4 Heegaard surface in 3-sphere.
Author provides an alternate proof of the free ribbon lemma.
Paper studies inscribed sphere and lines through centers of Apollonius spheres in n dimensions.
Sharp convergence theorem for sphere submanifolds proved.
In the 1-parameter family of Berger spheres S^3(a), a > 0 (S^3(1) is the round 3-sphere of radius 1) we classify the stable constant mean curvature spheres, showing that in some Berger spheres (a close to 0) there are unstable constant mean curvature spheres. Also, we classify the orientable compact stable constant mea…
We introduce and study a new class of homotopy spheres called Farrell-Jones spheres. Using Farrell-Jones sphere we construct examples of closed negatively curved manifolds , where or , which are homeomorphic but not diffeomorphic to complex hyperbolic manifolds, thereby giving a partial answer to a que…
In this paper we show that for m>n the set of cobordism classes of maps from m-sphere to n-sphere is trivial. The determination of the cobordism homotopy groups of spheres admits applications to the covers for spheres.
Study finds infinite families of Sasaki-Einstein metrics on spheres.
We show that among Seifert fibered integer homology spheres, Poincare sphere (with either orientation) is the only non-trivial example which has trivial Heegaard Floer homology. Together with an earlier result, this shows that if an integer homology sphere has trivial Heegaard Floer homology, then it is a connected sum…
We prove a Reeb sphere theorem for finite simple graphs. The result bridges two different definitions of spheres in graph theory. We also reformulate Morse conditions in terms of the center manifolds, the level surface graphs {f=f(x)} in the unit sphere S(x). In the Morse case these graphs are either spheres, the empty…
Study biharmonic hypersurfaces in spheres, proving unique continuation theorem.
Standard proved to be diffeomorphic to a curious homotopy sphere.
We provide a computer-assisted proof of the holomorphy of the quartic and the octic meromorphic differentials arising in the main Theorem 4.11 of our paper 'The Classification of Branched Willmore spheres in the -Sphere and the -Sphere' (arXiv:1706.01405), using the free mathematical software Sage.
New actions found on exotic spheres using group theory.
Here we generalize the Gromoll-Meyer construction of an exotic 7-sphere by producing geometric models of exotic 8, 10 and Kervaire spheres as quotients of sphere bundles over spheres by free isometric actions. We give a geometric application at the end.
New bounds and examples for sphere unknotting numbers.
We construct a new infinite family of models of exotic 7-spheres. These models are direct generalizations of the Gromoll-Meyer sphere. From their symmetries, geodesics and submanifolds half of them are closer to the standard 7-sphere than any other known model for an exotic 7-sphere.
Survey of Dupin hypersurfaces in Lie sphere geometry.