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.
Proves geodesic connections on 2-torus without invariant tori.
Given a closed, oriented surface, possibly with boundary, and a mapping class, we obtain sharp lower bounds on the number of fixed points of a surface symplectomorphism (i.e. area-preserving map) in the given mapping class, both with and without nondegeneracy assumptions on the fixed points. This generalizes the Poinca…
Area-preserving diffeomorphisms of a 2-disc can be regarded as time-1 maps of (non-autonomous) Hamiltonian flows on solid tori, periodic flow-lines of which define braid (conjugacy) classes, up to full twists. We examine the dynamics relative to such braid classes and define a braid Floer homology. This refinement of t…
We introduce large scale analogues of topological monotone and light maps, which we call coarsely monotone and coarsely light maps respectively. We show that these two classes of maps constitute a factorization system on the coarse category. We also show how coarsely monotone maps arise from a reflection in a similar w…
Study on biharmonic map heat flow with monotonicity formula.
In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all translated coordinate cones in R^n. In this paper we develop this theory further by d…
The paper explores methods to decompose periodic maps into Dehn twists.
Constructs differential models for twisted Spin^c-bordism and its dual, defining a new anomaly map.
Solves generalized twisted rabbit problems for higher degree polynomials.
The paper explores the twisted Rokhlin property in mapping class groups of surfaces.
In this paper, we introduce the stress-energy tensors of the partial energies E'(f) and E"(f) of maps between Kaehler manifolds. Assuming the domain manifolds poss some special exhaustion functions, we use these stress-energy tensors to establish some monotonicity formulae of the partial energies of pluriharmonic maps …
New quantity helps map homotopy classes in complex spaces.
This work clarifies different transport map constructions and their causal interpretations.
Study of codimension-1 embeddings in 3-manifolds using twist maps and push maps.
Develops moment map theory for twisted scalar curvature in Kähler geometry.
Calculates Dehn twist actions on conformal blocks for modular categories.
The Burau representation of the braid group can be used to recover the Alexander polynomial of the closure of a braid. We define twisted Burau maps and use them to compute twisted Alexander polynomials.
We give a small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. The difference between the number of the generators and a lower bound of numbers of generators for the twist subgroup by Dehn twists is one. The lower bounds is obtained from an argument of Hiros…
New method calibrates neural network predictions for better reliability.
We establish the Thom isomorphism in twisted K-theory for any real vector bundle and develop the push-forward map in twisted K-theory for any differentiable proper map (not necessarily K-oriented). The push-forward map generalizes the push-forward map in ordinary K-theory for any -oriented differentiable…
We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. The generating set consists of crosscap pushing maps along non-separating two-sided simple loops and squares of Dehn twists along non-separating two-sided simple closed curves. We also prove t…
New natural presentation of supergravity c-map using Hodge structures.
The paper derives Liouville theorems for various generalized maps on Riemannian manifolds.
We construct the geometric Baum-Connes assembly map for twisted Lie groupoids, that means for Lie groupoids together with a given groupoid equivariant principle bundle. The construction is based on the use of geometric deformation groupoids, these objects allow in particular to give a geometric construction of …
Locally maximizing orbits studied in twist maps and billiards.
We consider a twisted version of the Hurewicz map on the complement of a hyperplane arrangement. The purpose of this paper is to prove surjectivity of the twisted Hurewicz map under some genericity conditions. As a corollary, we also prove that a generic section of the complement of a hyperplane arrangement has non-tri…
The authors study in detail new types of varieties with degenerate Gauss maps: varieties with multiple foci and their particular case, the so-called twisted cones. They prove an existence theorem for twisted cones and describe their structure.
Shifts are not type-preserving on surface graphs.
The paper explores mapping class group quotients by Dehn twists and their representations.
New relation found in 4D symplectic mapping class group.
This is a PhD thesis in low-dimensional topology. Its main purpose is to examine so-called tête-à-tête twists. Those were defined by A'Campo and give an easy combinatorial description of certain mapping classes on surfaces with boundary. Whereas the well-known Dehn twists are twists around a simple closed curve, tête-à…
Paper examines Dehn twists on non-orientable surfaces and their limitations.
Holomorphic maps are a special case of Hermitian pluriharmonic maps between almost Hermitian manifolds.
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers via a Poisson point process with mean measure on the power set of . Each $E\in\cate$ has a least monotone cover in $\catf$, the collection of monotone subsets of $\cate$, an…
We give new upper bounds on the stable commutator lengths of Dehn twists in mapping class groups and new lower bounds on the stable commutator lengths of Dehn twists in hyperelliptic mapping class groups. In particular, we show that the stable commutator lengths of Dehn twists about a nonseparating and a separating cur…
Study on realizing subgroup twists in 3-manifolds.
This paper provides an infinite presentation for a subgroup of mapping class groups of non-orientable surfaces.
We show that our earlier work in \cite{LT05} extends to the twisted case, that is, we defined a notion of moment map and reduction in both twisted generalized complex geometry and twisted generalized Kähler geometry.
Study shows Dehn twist coefficients are consistent across different actions on surfaces.
Characterizes continuity of monotone functionals in mixed topology.
Boundary Dehn twists become trivial after abelianization.
We study subgroups of the mapping class group of the torus generated by powers generated by powers of Dehn twists. We give a criterion to show when a collection of powers Dehn twists generates a free group using the ping pong lemma. We show that the subgroup generated by three uniform powers of Dehn twists can be eithe…
Study spherical twists on K3 surfaces, compute their centers.
New framework for learning KR maps from data, ensuring stable generalization.
Growth rate of Dehn twist lattice points in Teichmüller space is slower than mapping class group lattice points.
We show that on a nonorientable surface of genus at least 7 any power of a Dehn twist is equal to a single commutator in the mapping class group and the same is true, under additional assumptions, for the twist subgroup, and also for the extended mapping class group of an orientable surface of genus at least 3.
The paper studies knots formed by twisting a circle around a base knot and conjectures a linear growth in crossing numbers.
We study monodromies of plane curve singularities and pseudo-periodic homeomorphisms of oriented surfaces with boundary, following an original idea of the first author: tête-à-tête graphs and twists. We completely characterize mapping classes that can be represented by tête-à-tête twists, and generalize the notion to b…