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 defines and classifies Cappell-Shaneson polynomials.
New examples of Cappell-Shaneson knot pairs with same Alexander polynomial found.
Gompf proposed a conjecture on Cappell-Shaneson matrices whose affirmative answer implies that all Cappell-Shaneson homotopy 4-spheres are diffeomorphic to the standard 4-sphere. We study Gompf conjecture on Cappell-Shaneson matrices using various algebraic number theoretic techniques. We find a hidden symmetry between…
We show that one of the Cappell-Shaneson knot complements admits an extraordinarily small triangulation, containing only two 4-dimensional simplices.
We show that an infinite sequence of homotopy 4-spheres constructed by Cappell-Shaneson are all diffeomorphic to S^4. This generalizes previous results of Akbulut-Kirby and Gompf.
New homotopy 4-spheres and real projective 4-spaces created.
New research finds 145 infinite families of CS spheres are standard.
Akbulut has recently shown that an infinite family of Cappell-Shaneson homotopy 4-spheres is diffeomorphic to the standard 4-sphere. In the present paper, a strictly larger family is shown to be standard by a simpler method. This new approach uses no Kirby calculus except through the relatively simple 1979 paper of Akb…
We show that the Cappell-Shaneson version of Pick's theorem for simple lattice polytopes is a consequence of a general relation between characteristic numbers of virtual submanifolds dual to the characteristic classes of a stably almost complex manifold. This relation is analogous to the miraculous cancellation formula…
New non-orientable 4-manifolds created via knotting operations.
In this paper, we investigate existence of inequivalent smooth structures on closed smooth non-orientable 4-manifolds building upon results of Akbulut, Cappell-Shaneson, Fintushel-Stern, Gompf, and Stolz. We add to the number of known constructions and provide new examples of exotic manifolds that are obtained as an ap…
The stable Andrews-Curtis conjecture in combinatorial group theory is the statement that every balanced presentation of the trivial group can be simplified to the trivial form by elementary moves corresponding to "handle-slides" together with "stabilization" moves. Schoenflies conjecture is the statement that the compl…
In 1987 S Cappell and J Shaneson constructed an s-cobordism H from the quaternionic 3-manifold Q to itself, and asked whether H or any of its covers are trivial product cobordism? In this paper we study H, and in particular show that its 8-fold cover is the product cobordism from S^3 to itself. We reduce the triviality…
Within its traditional range of perversity parameters, intersection cohomology is a topological invariant of pseudomanifolds. This is no longer true once one allows superperversities, in which case intersection cohomology may depend on the choice of the stratification by which it is defined. Topological invariance also…
We provide a generalization of the Deligne sheaf construction of intersection homology theory, and a corresponding generalization of Poincaré duality on pseudomanifolds, such that the Goresky-MacPherson, Goresky-Siegel, and Cappell-Shaneson duality theorems all arise as special cases. Unlike classical intersection homo…
While topologists have had possession of possible counterexamples to the smooth 4-dimensional Poincaré conjecture (SPC4) for over 30 years, until recently no invariant has existed which could potentially distinguish these examples from the standard 4-sphere. Rasmussen's s-invariant, a slice obstruction within the gener…
New -polynomial distinguishes knotoid diagrams not previously possible.
The paper studies polynomials and ideals from colored Jones polynomials for links.
Paper constructs a new approach to extract Affine Index Polynomial from Sawollek Polynomial.
This paper studies the Riley polynomial of 2-bridge knots using Chebyshev polynomials.
Novel knot polynomials from Gaussian calculus show half vanish and determine Jones polynomials.
Developed algorithms to compute three polynomial invariants of veering triangulations.
Study links weaving knots with polynomial coefficients and lattice numbers.
Study revisits Alexander-Conway and Kauffman bracket polynomials for pretzel links.
Paper connects AJ conjecture and colored Jones polynomial potential function.
Associated with each oriented link is the two variable Homflypt polynomial. The Morton-Franks-Williams (MFW) inequality gives rise to an expression for the Homflypt polynomial with MFW coefficient polynomials. These MFW coefficient polynomials are labelled in a braid-dependent manner and may be zero, but display a numb…
This paper investigates the equivalence between Yamada polynomial and Jones polynomial of associated links for brunnian θ-curves.
The taut polynomial equals a twisted Alexander polynomial.
Quantum polynomials are derived from a specific tribracket structure.
We classify rooted trees which have strictly unimodal q-polynomials (plucking polynomial). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients. We discuss which polynomials can be realized as plucking polynomial…
New polynomials detect non-rotatable knotoid shapes.
Innovates polynomial invariant for tribrackets.
Researchers extend Alexander polynomial to knotoids and linkoids.
Unified ADO and colored Jones polynomials for knots.
Generalized quandle polynomial used for stuquandles, stuck links, and RNA folding.
Study Alexander polynomials of ribbon and virtual knots using ribbon's intrinsic singularity.
We study rack polynomials and the link invariants they define. We show that constant action racks are classified by their generalized rack polynomials and show that -quandles are not classified by their generalized quandle polynomials. We use subrack polynomials to define enhanced rack counting invariants, gen…
In this paper, we define some polynomial invariants for virtual knots and links. In the first part we use Manturov's parity axioms to obtain a new polynomial invariant of virtual knots. This invariant can be regarded as a generalization of the odd writhe polynomial defined by the first author. The relation between this…
Paper computes Alexander polynomials for arborescent links.
Jones polynomials derived from K-theory of a cluster algebra.
We study relationships between the colored Jones polynomial and the A-polynomial of a knot. We establish for a large class of 2-bridge knots the AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial. Along the way we also calculate the Kauffman bracket skein module of all 2-brid…
The interior polynomial is an invariant of bipartite graphs, and a part of the HOMFLY polynomial of a special alternating link coincides with the interior polynomial of the Seifert graph of the link. We extend the interior polynomial to signed bipartite graphs, and we show that, in the planar case, it is equal to a par…
New skein theory for Links-Gould polynomial simplifies link evaluations.
Prime knots of genus one admitting diagram with at most five classical crossings were classified by Akimova and Matveev in 2014. In 2018 Kaur, Prabhakar and Vesnin introduced families of L-polynomials and F-polynomials for virtual knots which are generalizations of affine index polynomial. Here we introduce a notion of…
Jones polynomials have infinitely many roots of unity as zeros.
Two categorifications are given for the arrow polynomial, an extension of the Kauffman bracket polynomial for virtual knots. The arrow polynomial extends the bracket polynomial to infinitely many variables, each variable corresponding to an integer {\it arrow number} calculated from each loop in an oriented state summa…
Study connects group invariants through outer automorphisms and polynomial relations.
Minimal polynomial found for Riemannian C_0-spaces.