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.
The paper uses Heegaard Floer homology to find lower bounds on link genera.
Study extends knot genus results to two-component alternating links.
Every link is shown to be presentable as a boundary of an unknotted flat banded surface. A (flat) banded link is defined as a boundary of an unknotted (flat) banded surface. A link's (flat) band index is defined as the minimum number of bands required to present the link as boundaries of an unknotted (flat) banded surf…
We define the basket number, the flat plumbing number and the flat plumbing basket number of a link. Then we provide some upperbounds for these plumbing numbers by using Seifert's algorithm. We study the relation between these plumbing numbers and the genera of links.
We show that nontrivial classical pretzel knots L(p,q,r) are hyperbolic with eight exceptions which are torus knots. We find Conway polynomials of n-pretzel links using a new computation tree. As applications, we compute the genera of n-pretzel links using these polynomials and find the basket number of pretzel links b…
We prove that the genus of the Turaev surface of a link diagram is determined by a graph whose vertices correspond to the boundary components of the maximal alternating regions of the link diagram. Furthermore, we use these graphs to classify link diagrams whose Turaev surface has genus one or two, and we prove that si…
We introduce a new link invariant called the algebraic genus, which gives an upper bound for the topological slice genus of links. In fact, the algebraic genus is an upper bound for another version of the slice genus proposed here: the minimal genus of a surface in the four-ball whose complement has infinite cyclic fun…
The paper offers new methods to determine if certain 3D links can be formed by intersecting spheres in 4D space.
The existence of basket, flat plumbing and flat plumbing basket surfaces of a link was first proven from a braid representative of the link. In the present article, we show the existence of such surfaces from an induced graph of the link. Consequently, we define the basket number, flat plumbing number and flat plumbing…
Ozsvath and Szabo proved that knot Floer homology determines the genera of knots in S^3. We will generalize this deep result to links in homology 3-spheres, by adapting their method. Our proof relies on a result of Gabai and some constructions related to foliations. We also interpret a theorem of Kauffman in the world …
Defines a Rasmussen invariant for links in RP^3.
First time projective elliptic genera constructed for oriented manifolds.
The paper constructs exotic surface links in 4-ball, proving their Brunnian nature.
We give a new proof that the Levine-Tristram signatures of a link give lower bounds for the minimal sum of the genera of a collection of oriented, locally flat, disjointly embedded surfaces that the link can bound in the 4-ball. We call this minimal sum the 4-genus of the link. We also extend a theorem of Cochran, Frie…
New vanishing theorems for genera derived under almost nonnegative Ricci curvature.
We determine the PSL_2(C) and SL_2(C) character varieties of the once-punctured torus bundles with tunnel number one, i.e. the once-punctured torus bundles that arise from filling one boundary component of the Whitehead link exterior. In particular, we determine `natural' models for these algebraic sets, identify them …
Authors show that genus defects of Hopf arborescent links are decidable.
Simplified proof of complex manifold Todd genera invariance.
Paper constructs Witten and elliptic genera for noncompact manifolds with proper actions.
We generalise work of Young-Eun Choi to the setting of ideal triangulations with vertex links of arbitrary genus, showing that the set of all (possibly incomplete) hyperbolic cone-manifold structures realised by positively oriented hyperbolic ideal tetrahedra on a given topological ideal triangulation and with prescrib…
The paper defines a new invariant for links and uses it to show non-sliceness.
Study intersection polynomials of long virtual knots with supporting genera.
New findings on knot genera using advanced techniques.
Study proves Witten genera vanish for certain manifolds, supporting a conjecture.
We give infinitely many examples of 2-bridge knots for which the topological and smooth slice genera differ. The smallest of these is the 12-crossing knot . These also provide the first known examples of alternating knots for which the smooth and topological genera differ.
Rigidity of elliptic genera proven for non-spin manifolds with -action.
New elliptic genera defined for spin manifolds.
For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higher-order genera in terms of certain von Neumann -invariants, which we call higher-order signatures. The higher-order genera o…
Each ruling of a Legendrian link can be naturally treated as a surface. For knots, the ruling is 2-graded if and only if the surface is orientable. For 2-graded rulings of homogeneous (in particular, alternating) knots, we prove that the genus of this surface is at most the genus of the knot. While this is not true in …
This paper analyzes the distribution of genera in 2-bridge knots and proves their asymptotic normality.
We obtain general formulae expressing Hirzebruch genera of a manifold with Z/p-action in terms of invariants of this action (the sets of weights of fixed points). As an illustration, we consider numerous particular cases of well-known genera, in particular, the elliptic genus. We also describe the connection with the s…
The paper studies complex genera and related geometric applications, deriving formulas for multiple zeta values.
The paper studies geometric properties of higher genera for proper Lie group actions.
The paper introduces new inequalities for knots in 4D cobordisms.
I. Hambleton, A. Korzeniewski and A. Ranicki proved that the signature of a fibre bundle of closed, connected, compatibly oriented PL manifolds is always multiplicative modulo 4. In this paper, we consider the Hirzebruch -genera for odd integers for a smooth fiber bundle such that the base, fibre, and total sp…
It is a conjecture that the signature of a positive link is bounded below by an increasing function of its negated Euler characteristic. In relation to this conjecture, we apply the generator description for canonical genus to show that the boundedness of the genera of positive knots with given signature can be algorit…
This paper contains the results of efforts to determine values of the smooth and the topological slice genus of 11- and 12-crossing knots. Upper bounds for these genera were produced by using a computer to search for genus one concordances between knots. For the topological slice genus further upper bounds were produce…
Generics extended to new cohomologies.
We study fixed points of smooth torus actions on closed manifolds using fixed point formulas and equivariant elliptic genera. We also give applications to positively curved Riemannian manifolds with symmetry.
We prove the vanishing of higher A-hat-genera, in the sense of Browder and Hsiang, on smooth manifolds with effective circle actions and with finite second and fourth homotopy groups
Identifies doubly slice genera for 2909 prime knots with up to 12 crossings.
Study String structures using algebraic topology and generalize Witten genera.
In the paper we describe obstructions for the existence of symplectic and Hamiltonian symplectic circle actions on closed compact manifolds in terms of Hirzebruch genera and relations between differential and homotopic invariants of such manifolds.
Gromov-Witten invariants linked to flat connections and Donaldson-Thomas invariants.
The paper defines new knot genera and finds bounds for stabilization distances.
We prove several vanishing theorems for a class of generalized elliptic genera on foliated manifolds, by using classical equivariant index theory. The main techniques are the use of the Jacobi theta-functions and the construction of a new class of elliptic operators associated to foliations.
The broken genera are orientation preserving diffeomorphism invariants of closed oriented 4-manifolds, defined via broken Lefschetz fibrations. We study the properties of the broken genera invariants, and calculate them for various 4-manifolds, while showing that the invariants are sensitive to exotic smooth structures…
Presentations for involutions on non-orientable surfaces up to genus 5.