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.
Multisections generalize Heegaard splittings and trisections to higher dimensions.
New method to encode Weinstein 4-manifolds using multisections with divides.
The paper constructs multisections for m-spun 3-manifolds in higher dimensions.
New method for decomposing manifolds into 1-handlebodies.
Efficient multisections found for odd-dimensional tori.
Paper proves uniqueness of bridge multisections for surfaces in 4-space.
New method to compute homology and intersection form of 4-manifolds.
Study of curves in rational surfaces using multisections and torus actions.
The study shows manifolds with special generic maps also have nice multisections.
Multisections generalize trisections for 4-manifolds, allowing complex operations and explicit diagrams.
In this article, we characterize isomorphism classes of Lefschetz fibrations with multisections via their monodromy factorizations. We prove that two Lefschetz fibrations with multisections are isomorphic if and only if their monodromy factorizations in the relevant mapping class groups are related to each other by a f…
We initiate a study of positive multisections of Lefschetz fibrations via positive factorizations in framed mapping class groups of surfaces. Using our methods, one can effectively capture various interesting symplectic surfaces in symplectic 4-manifolds as multisections, such as Seiberg-Witten basic classes and except…
We give examples of foliations that answer two questions posed by Mitsumatsu and Vogt about the genus minimising properties of closed leaves of 2-dimensional foliations on 4-manifolds. By studying stable commutator lengths in certain stable mapping class groups, we also answer an asymptotic version of another question …
Recently Gay and Kirby described a new decomposition of smooth closed -manifolds called a trisection. This paper generalises Heegaard splittings of -manifolds and trisections of -manifolds to all dimensions, using triangulations as a key tool. In particular, we prove that every closed piecewise linear -mani…
Defines pants distance for knotted surfaces in 4-manifolds.
Study of 3-manifolds in 5-sphere using bridge decompositions.
New invariant defined for Weinstein domains, related to Kirby-Thompson's invariant.
We show that the "geometric models of matter" approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold singularities along embedded 2-dimensional surfaces. The anyon states arise through…
Gay and Kirby introduced the notion of a trisection of a smooth 4-manifold, which is a decomposition of the 4-manifold into three elementary pieces. Rubinstein and Tillmann later extended this idea to construct multisections of piecewise-linear (PL) manifolds in all dimensions. Given a PL manifold of dimension ,…
The paper finds infinitely many 4-manifolds with non-isotopic sections.
In this paper we use continuous family of multisections of the moduli space of pseudo holomorphic discs to partially improve, in the case of real coefficient, the construction of Lagrangian Floer cohomology of which the author developed jointly with Oh-Ohta-Ono. Namely we associate cyclically symmetric filtered A infin…
4-manifolds can be uniquely described as loops of Morse functions.
We analyze a notion of multiple valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some useful techniques for dealing with multiple valued functions" and generalizes Almgren's -valued functions. We study some relevant properties o…
Let M be a compact oriented even-dimensional manifold. This note constructs a compact symplectic manifold S of the same dimension and a map f from S to M of strictly positive degree. The construction relies on two deep results: the first is a theorem of Ontaneda that gives a Riemannian manifold N of tightly pinched neg…
We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure. We prove that our algorithm achieves exact recovery of the latent communities, up to the information-theoretic limits determined by Abbe and Sandon (…
Cieliebak, Mundet i Riera and Salamon recently formulated a definition of branched submanifold of Euclidean space in connection with their discussion of multivalued sections and the Euler class. This note proposes an intrinsic definition of a weighted branched manifold Z that is obtained from the usual definition of or…
Closed Riemannian 4 or 5-manifolds contain branched immersed closed minimal surfaces.
New methods decompose manifolds into submanifolds via fold maps.
New tools classify symplectic fillings of contact 3-manifolds.
We consider the problem of identifying underlying community-like structures in graphs. Towards this end we study the Stochastic Block Model (SBM) on -clusters: a random model on vertices, partitioned in equal sized clusters, with edges sampled independently across clusters with probability and within …
Study symplectic fillings of sandwiched singularities.