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.
Simplified proof of spin^c structures using twistor spaces.
New proofs for complex Hopf manifolds using geometric structures.
The controlled end and h-cobrodism theorems (Ends of maps I, 1979) are used to give quick proofs of the Top/PL and PL/DIFF product structure theorems.
After surveying existing proofs that every closed, orientable 3-manifold is parallelizable, we give three proofs using minimal background. In particular, our proofs use neither spin structures nor the theory of Stiefel-Whitney classes.
This is an expository paper giving a proof of the existence and uniqueness of smooth structures (hence also PL structures) on topological surfaces. Most published proofs rely on the topological Schoenflies theorem, but here we use instead the Kirby torus trick. This has the advantage of reducing the point-set topology …
New model shows hierarchical proof structure helps theorem provers.
New proof shows 4-manifolds can't support complex structures.
The aim of this paper is to give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. This theorem asserts that simply-connected five-manifolds admit a contact structure in every homotopy class of almost contact structures. Our proof uses the open book constructio…
Proof of contact structure from taut foliation for certain knots.
We give a geometric proof of existence of Whitney stratifications of definable sets in o-minimal structures.
Study simplifies classification of foliations with specific geometric structures.
Proof that convex structures on manifolds are open and closed.
Counterexample and new proof for curvature varifolds.
In 1989, Y. Eliashberg proved that two overtwisted contact structures on a closed oriented 3-manifold are isotopic if and only if they are homotopic as 2-plane fields. We provide an alternative proof of this theorem using the convex surface theory and bypasses.
We give a new proof of Gromov's theorem that any finitely generated group of polynomial growth has a finite index nilpotent subgroup. Unlike the original proof, it does not rely on the Montgomery-Zippin-Yamabe structure theory of locally compact groups.
We give a proof of, for the case of contact structures defined by global contact 1-forms, a Theorem stated by Eliashberg that for any overtwisted contact structure on a closed 3-manifold, its contact homology is 0. A different proof is also outlined in the appendix by Yakov Eliashberg.
Proves and tests methods for learning time-series with breaks.
We describe the flat surfaces with flat normal bundle and regular Gauss map immersed in R^4 using spinors and Lorentz numbers. We obtain a new proof of the local structure of these surfaces. We also study the flat tori in the sphere S^3 and obtain a new representation formula. We then deduce new proofs of their global …
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of classifier. Though such a proof appears simple on paper, analytic and measure-theoret…
Contact round surgery of contact 3-manifolds is introduced in this paper. By using this method, an alternative proof of the existence of a contact structure on any closed orientable 3-manifold is given. It is also proved that any contact structure on any closed orientable 3-manifold is constructed from the standard con…
The aim of this note is to provide an intrinsic proof of the Gauss--Bonnet theorem without invoking triangulations, which is achieved by exploiting complex structures.
New proof of generalized Chow-Rashevskii theorem for non-linear systems.
New proof shows lower bound for commutator length in RAAGs.
We outline a proof of a remarkable conjecture of Labastida-Mari{ñ}o-Ooguri-Vafa about certain new algebraic structures of quantum link invariants and the integrality of infinite family of new topological invariants. Our method is based on the cut-and-join analysis and a special rational ring characterizing the structur…
We give a short, simple and conceptual proof, based on spin structures, of sphere eversion: an embedded 2-sphere in can be turned inside out by regular homotopy. Ingredients of this eversion are seamlessly connected. We also give the mathematical origins of the proof: the Hopf fibration, and the topological struc…
Kuranishi's proof of complex deformation theory revisited
New proof shows certain manifolds cannot have real projective structure.
New proof shows unique symplectic fillings for certain surface singularity links.
Proof shows volume equals integral points for certain manifolds.
We show that any 4-manifold, after surgery on a curve, admits an achiral Lefschetz fibration. In particular, we show that the connected sum of any simply connected 4-manifold with a 2-sphere bundle over the 2-sphere will admit an achiral Lefschetz fibration. We also show these surgered manifolds admit near-symplectic s…
First geometric proof of the flyping theorem.
New proof for quaternionic structures on specific manifolds via automorphisms.
This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame which encompasses families of arrangements. The frame uses the notion of matroids. For the proof of the existence of the potentials, a power series ansatz is made. The proof that it works requires that ce…
Improved estimates for -structures on a specific manifold.
In this paper, we show that Gromov-Thurston's principle works for hyperbolic 3-manifolds of infinite volume and with finitely generated fundamental group. As an application, we have a new proof of Ending Lamination Theorem. Our proof essentially relays only on Maximum Volume Law for hyperbolic 3-simplices.
We will simplify the earlier proofs of Perelman's collapsing theorem of 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's semi-convex analysis of distance functions to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelma…
By use of a natural map introduced recently by the first and third authors from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the small differentiable deformation of this manifold, we will give a power series proof for Kodaira-Spencer's local stability theorem of Kä…
Geometrically constructs dilogarithm from Chern-Simons theory.
A simple proof shows standard billiard for certain convex domains.
We provide a detailed proof of Hawking's singularity theorem in the regularity class , i.e., for spacetime metrics possessing locally Lipschitz continuous first derivatives. The proof uses recent results in -causality theory and is based on regularisation techniques adapted to the causal structure.
New proof of Lie algebroid action equivalence and integrability.
No fair and strategy-proof automated market maker exists for more than two assets.
Sharp estimates proved for complex Monge-Ampère equations.
Given a special Kahler manifold M, we give a new, direct proof of the relationship between the quaternionic structure on its cotangent bundle and the variation of Hodge structures on the complexification of TM.
Proves Giroux Correspondence in 3D using Heegaard splittings.
This research classifies invariant complex structures and Kähler metrics on principal bundles.
Using equivariant Toeplitz operator calculus, we give a new proof of the Atiyah-Weinstein conjecture on the index of Fourier integral operators and the relative index of CR structures.
Spin-structures on real Bott manifolds with Kähler structure are characterized.