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.
Lower bounds on rational slice genus using Heegaard Floer invariants.
The study calculates the average genus of rational knots and links.
The paper reconfirms a lower bound on rational genus using Heegaard Floer homology.
Local knots can't bound smaller surfaces in rational homology 3-spheres.
Study eigenvalues of curvature operators to annihilate cobordism invariants.
Proves existence of Lefschetz fibrations with arbitrary slopes.
The genus of satellite tunnel number one knots and torti-rational knots is computed using the tools introduced by Floyd and Hatcher. An implementation of an algorithm is given to compute genus and slopes of minimal genus Seifert surfaces for such knots.
We prove that rational homology of the Torelli group of genus g is infinite dimensional, provided g>6. This means that rational homology of the Torelli space of genus g>6 is infinite dimensional. The Torelli groups with marked points are also considered. In addition, we prove that rational homology of the subgroup of t…
If K is a rationally null-homologous knot in a 3-manifold M, the rational genus of K is the infimum of -χ(S)/2p over all embedded orientable surfaces S in the complement of K whose boundary wraps p times around K for some p (hereafter: S is a p-Seifert surface for K). Knots with very small rational genus can be constru…
Given a one-dimensional homology class in a lens space, a question related to the Berge conjecture on lens space surgeries is to determine all knots realizing the minimal rational genus of all knots in this homology class. It is known that simple knots are rational genus minimizers. In this paper, we construct many non…
Given an element in the first homology of a rational homology 3-sphere , one can consider the minimal rational genus of all knots in this homology class. This defines a function on , which was introduced by Turaev as an analogue of Thurston norm. We will give a lower bound for this function usi…
Homology of surface coverings solved for genus 3 and above.
Using the Heegaard Floer homology of Ozsvath and Szabo we investigate obstructions to definite intersection pairings bounded by rational homology spheres. As an application we obtain new lower bounds for the four-ball genus of Montesinos links.
New model shows average genus of 2-bridge knots grows linearly with crossing number.
Generalizes Lefschetz fibrations with rational homology disk smoothings.
Flexible knot construction for low genus surfaces.
Study counts specific surfaces in Montesinos knots with 4 rational tangles.
Torelli group's second homology is finite for large genus surfaces.
This paper proves an upper limit on rational points on curves.
Ricci-positive manifolds span the kernel of the -genus in rational Spin bordism.
Study of curves in rational surfaces using multisections and torus actions.
The rational cohomology ring of A_3, the moduli space of abelian 3-folds is computed. This is isomorphic to the the rational cohomology ring of the group Sp_3(Z) of 6x6 integral symplectic matrices. The main ingredients in the computation are (1) Looijenga's computation of the rational cohomology ring of M_3, the modul…
We describe Milnor open books and Legendrian surgery diagrams for canonical contact structures of links of some rational surface singularities. We also describe an infinite family of Milnor fillable contact 3-manifolds so that the Milnor genus (resp. Milnor norm) is strictly greater than the support genus (resp. suppor…
Study of pseudo-Anosov actions on -character variety for genus 2 surfaces.
Classifies 4-manifolds with genus one horizontal handlebody decomposition.
A torti-rational knot, denoted by K(2a,b|r), is a knot obtained from the 2-bridge link B(2a,b) by applying Dehn twists an arbitrary number of times, r, along one component of B(2a,b). We determine the genus of K(2a,b|r) and solve a question of when K(2a,b|r) is fibred. In most cases, the Alexander polynomials determine…
In this paper, the symplectic genus for any 2-dimensional class in a 4-manifold admitting a symplectic structure is introduced, and its relation with the minimal genus is studied. It is used to describe which classes in rational and irrational ruled manifolds are realized by connected symplectic surfaces. In particular…
We provide a new obstruction for a rational homology 3-sphere to arise by Dehn surgery on a given knot in the 3-sphere. The obstruction takes the form of an inequality involving the genus of the knot, the surgery coefficient, and a count of L-structures on the 3-manifold, that is spin-c structures with the simplest pos…
We show that hyperelliptic symplectic Lefschetz fibrations are symplectically birational to two-fold covers of rational ruled surfaces, branched in a symplectically embedded surface. This reduces the classification of genus 2 fibrations to the classification of certain symplectic submanifolds in rational ruled surfaces…
Paper computes rational cohomology of spin hyperelliptic mapping class groups.
Knot genus problem solved for all 3-manifolds.
We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings in terms of their generating functions. We show in particular how Fibonacci numb…
Study shows unbounded Pontryagin numbers on curved manifolds.
New knots found that are 4-genus minimal.
We study Nakai-Moishezon type question and Donaldson's "tamed to compatible" question for almost complex structures on rational four manifolds. By extending Taubes' subvarieties--current--form technique to nef genus classes, we give affirmative answers of these two questions for all tamed almost complex structu…
We give asymptotic bounds for the optimal Lipschitz constants for the systole map from the Teichmuller space to the curve complex. We give similar results to those known for closed surfaces in the cases when the genus is fixed or the ratio of genus and punctures is a rational number.
Smooth HP^2 bundle over S^4 with nontrivial A-genus found.
We consider closed acylindrical surfaces in 3-manifolds and in knot and link complements, and show that the genus of these surfaces is bounded linearly by the number of tetrahedra in the triangulation of the manifold and by the number of rational (or alternating) tangles in a projection of a link (or knot). For each g …
The study examines dynamics on SU(2)-representation varieties for surfaces and non-orientable surfaces.
We show that when the genus and punctures of a surface are directly proportional by some rational number the minimal asymptotic translation length in the curve complex has behavior inverse to the square of the Euler characteristic. We also show that when the genus is fixed and the number of punctures varies the behavio…
We complete the remaining cases of the conjecture predicting existence of infinitely many rational curves on K3 surfaces in characteristic zero, prove almost all cases in positive characteristic and improve the proofs of the previously known cases. To achieve this, we introduce two new techniques in the deformation the…
Study shows compact mapping class groups of infinite type surfaces are never perfect.
The paper shows knots with specific properties have smaller 4-genus.
We exhibit a finitely generated group $\M$ whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface $\su$ of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus with bo…
The study creates symplectic Lefschetz fibrations and rational blowdowns for new 4-manifolds.
In this article, we construct a genus- or genus- positive allowable Lefschetz fibration on any minimal symplectic filling of the link of non-cyclic quotient surface singularities. As a byproduct, we also show that any minimal symplectic filling of the link of quotient surface singularities can be obtained from a …
Stability in homology of moduli spaces of admissible covers.
Ozsvath and Szabo conjectured that knot Floer homology detects fibred knots. We propose a strategy to approach this conjecture based on Gabai's theory of sutured manifold decomposition and contact topology. We implement this strategy for genus-one knots, obtaining as a corollary that, if rational surgery on a knot …