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.
Category theory generalizes finite type invariants using diagrams systems.
Enhances biquandle counting invariant using finite type enhancements.
The study identifies helicoids and spheres as the only finite III-type ruled and quadric surfaces.
We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's higher order homotopy invariants and show that they are also, in a sense, of finite t…
Submanifolds of coordinate finite-type were introduced in HV1. A submanifold of a Euclidean space is called a coordinate finite-type submanifold if its coordinate functions are eigenfunctions of Δ. In the present study we consider coordinate finite-type surfaces in E^4. We give necessary and sufficient conditions for g…
Finite-type surfaces have a topological Hopf property.
Defines finite type Multivalued Shape using hyperspaces.
New invariant fully describes finite type invariants of knots in homology 3-spheres.
Finite type curves are asymptotic lines of plane fields, with examples.
Compact manifolds with boundary have finite type mapping class groups.
We observe that most known results of the form "v is not a finite-type invariant" follow from two basic theorems. Among those invariants which are not of finite type, we discuss examples which are "ft-independent" and examples which are not. We introduce (n,q)-finite invariants, which are generalizations of finite-type…
Homotopy classes of nanowords and nanophrases are combinatorial generalizations of virtual knots and links. Goussarov, Polyak and Viro defined finite type invariants for virtual knots and links via semi-virtual crossings. We extend their definition to nanowords and nanophrases. We study finite type invariants of low de…
Paper shows 3D hyperbolic manifolds are uniquely identified by their finite groups.
Finite type invariants separate PL links in 3D space.
Paper explores hyperbolic groups with unique subgroup properties.
Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite type invariants from the `cubic' point of view. Finite type invariants of knots and homology 3-spheres fit perfectly into this conception. In …
A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for manifolds with large first betti number, encompassing much of the complexity of Ohtsuki'…
Proofs for Gauss map properties on surfaces with finite geometric type.
Study surfaces of finite Chen-type using Beltrami operators.
Characterizes monodromies of projective structures on finite-type surfaces.
Delta finite-type invariants are defined analogously to finite-type invariants, using delta moves instead of crossing changes. We show that they are closely related to the lower central series of the commutator subgroup of the pure braid group.
Study on compact and finite-type support in mapping class group homology.
Only finitely many rational multiples of π are angles between geodesics on hyperbolic surfaces.
Finite rigid sets found in complex of curves for surfaces.
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject had been collected in author's book [Total mean curvature and sub manifolds of finite type, World Scientific, NJ, 1984]. A list of ten open problems and three conjectures on submanifolds of finite type was…
Study finds many Lagrangian fillings for certain Legendrian links.
In this paper, we define finite type invariants for cyclic equivalence classes of nanophrases and construct the universal ones. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold's basic invariants to signed words are finite type invar…
A smooth four manifold is of finite type if its Donaldson invariant satisfies D((x^2-4)^r)=0. We prove that every simply connected manifold is of finite type by using the structure of Donaldson invariants in the presence of immersed spheres. More precisely we prove that if a manifold X contains an immersed sphere w…
Goussarov, Polyak, and Viro proved that finite type invariants of knots are ``finitely multi-local'', meaning that on a knot diagram, sums of quantities, defined by local information, determine the value of the knot invariant. The result implies the existence of Gauss diagram combinatorial formulas for finite type inva…
4-manifolds with specific groups have unique homotopy types.
This paper studies finite type invariants for welded string links and ribbon tubes, showing characterizations and algebraic structures.
Study finite singularities in G2 structure flows using Shi-type estimates.
Study on Gauss map surfaces in 3D space, focusing on anchor rings.
In this paper, we give a complete set of finite type string link invariants of degree <5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closure of (cabled) string links. We show that finite type invariants classify string links up to …
This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics
Efficient algorithm computes knot invariants quickly.
Study finite time singularities in Ricci flow with bounded scalar curvature.
In this paper, it is shown that there are no nonconstant Goussarov-Polyak-Viro finite-type invariants that are invariant under the virtualization move. As an immediate corollary, we obtain the theorem which states none of the Birman coefficients of the Jones-Kauffman polynomial are of GPV finite type.
The paper proves finite topological type theorems for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume.
The study proves Gromov hyperbolicity for certain complex domains.
Finite type and finitely generated homotopy groups for manifold automorphisms.
We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.
Bar-Natan used Chinese characters to show that finite type invariants classify string links up to homotopy. In this paper, I construct the correct spaces of chord diagrams and Chinese characters for links up to homotopy. I use these spaces to show that the only rational finite type invariants of link homotopy are the p…
Finite-type k-surfaces in hyperbolic space have finite genus and cusp-like ends.
Artin groups of finite type are not as well understood as braid groups. This is due to the additional geometric properties of braid groups coming from their close connection to mapping class groups. For each Artin group of finite type, we construct a space (simplicial complex) analogous to Teichmueller space that satis…
Study proves all free boundary CMC annuli are of finite type.
We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9 components, there must exist finite type homotopy invariants which are not products of the linking numbers. This corrects previous errors of…
The paper studies properties of mapping class groups for surfaces with infinite fundamental groups.