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.
Algorithm calculates Hopf invariant for simplicial mappings.
The Hopf invariant is linked to null-homotopy properties of maps.
The Kuperberg invariant is a topological invariant of closed 3-manifolds based on finite-dimensional Hopf algebras. In this paper, we initiate the program of constructing 4-manifold invariants in the spirit of Kuperberg's 3-manifold invariant. We utilize a structure called a Hopf triplet, which consists of three Hopf a…
Futaki invariant vanishes on Hopf manifolds.
Paper proves unbounded stabilization heights of fiber surfaces using Hopf invariant.
Involutory Hopf group-coalgebras provide new invariants for 4-manifold bundles.
Invariants for 4-manifolds from Hopf group-algebras.
Paper connects two invariants of 3D manifolds using Hopf algebras.
New gauge invariants from framed 3-manifolds match Hopf algebra indicators.
This paper updates knot invariants using Hopf algebras and categorifies their structure.
New tool: relative Hopf invariant for Poincaré surgery.
The Kuperberg invariant is shown to be gauge invariant for certain framed 3-manifolds.
Invariants of 3-manifolds using modified Hopf G-coalgebra.
New Hopf algebras help classify 4D shapes.
New quantum invariant for framed 3-manifolds using ideal triangulations.
We prove a 20-year-old conjecture concerning two quantum invariants of three manifolds that are constructed from finite dimensional Hopf algebras, namely, the Kuperberg invariant and the Hennings-Kauffman-Radford invariant. The two invariants can be viewed as a non-semisimple generalization of the Turaev-Viro-Barrett-W…
Given a group G, we use involutary Hopf G-coalgebras to define a scalar invariant of flat G-bundles over 3-manifolds. When G=1, this invariant equals to the one of 3-manifolds constructed by Kuperberg from involutary Hopf algebras. We give examples which show that this invariant is not trivial.
Crane and Frenkel proposed a state sum invariant for triangulated 4-manifolds.They defined and used new algebraic structures called Hopf categories for their construction. Crane and Yetter studied Hopf categories and gave some examples using group cocycles that are associated to the Drinfeld double of a finite group. I…
We present an invariant of connected and oriented closed 3-manifolds based on a coribbon Weak Hopf Algebra H with a suitable left-integral. Our invariant can be understood as the generalization to Weak Hopf Algebras of the Hennings-Kauffman-Radford evaluation of an unoriented framed link using a dual quantum-trace. Thi…
New invariant calculates 4-manifolds using trisection diagrams and combings.
Quantum invariants for fibered links determined by genus and Hopf invariant.
We compute the Casson-Lin invariant for the Hopf link and determine the sign in the formula of Harper and Saveliev relating this invariant to the linking number.
Study knot invariants to deduce Hopf invariant and propose a slope conjecture.
The geometric Hopf invariant of a stable map F is a stable Z_2-equivariant map h(F) such that the stable Z_2-equivariant homotopy class of h(F) is the primary obstruction to F being homotopic to an unstable map. In this paper we express the geometric Hopf invariant of the Umkehr map F of an immersion f:M^m \to N^n in t…
In this paper we define the bi-orthogonal sectional curvature and we present two modified Yamabe invariants for compact 4-dimensional manifolds. In particular we obtained a relationship between one of these invariants and a Hopf conjecture.
Aguiar and Ardila defined the Hopf monoid GP of generalized permutahedra and showed that it contains many submonoids that correspond to combinatorial objects. They also give a basic polynomial invariant of generalized permutahedra, which then specializes to the submonoids. We define the Hopf monoid of directed graphs a…
The Reshetikhin-Turaev invariant, Turaev's TQFT, and many related constructions rely on the encoding of certain tangles (n-string links, or ribbon n-handles) as n-forms on the coend of a ribbon category. We introduce the monoidal category of Hopf diagrams, and describe a universal encoding of ribbon string links as Hop…
The Drinfeld double of a finite dimensional Hopf algebra is a quasi-triangular Hopf algebra with the canonical element as the universal -matrix, and one can obtain a ribbon Hopf algebra by adding the ribbon element. The universal quantum invariant of framed links is constructed using a ribbon Hopf algebra. In that c…
In the 90s, based on presentations of 3-manifolds by Heegaard diagrams, Kuperberg associated a scalar invariant of 3-manifolds to each finite dimensional involutory Hopf algebra over a field. We generalize this construction to the case of involutory Hopf algebras in arbitrary symmetric monoidal categories admitting cer…
Refines a tangle invariant using XC-algebras.
Using a power sum (boson) realization for the Macdonald operators, we investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the homological invariants of the colored Hopf link, which include Khovanov-Rozansky homology as a special case. We prove the polynomiality of the invariants obtained by GIKV's proposa…
A handlebody-knot is a handlebody embedded in the 3-sphere. We establish a uniform method to construct invariants for handlebody-links. We introduce the category of handlebody-tangles and present it by generators and relations. The result tells us that every functor on that gives rise to inv…
Modified Hennings invariant defined using quantum groups and integrals.
Study extends knot polynomials to links, identifying them with known invariants.
We introduce a Hopf algebroid associated to a proper Lie group action on a smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is equal to the de Rham cohomology of invariant differential forms. When the action is cocompact, we develop a generalized Hodge theory for the de Rham cohomology of inv…
New framework models high-Hopf-index hopfions using generalized fold maps.
Invariants for 3-manifolds with embedded links using Hopf algebras.
Oleg Viro studied in arXiv:math/0204290 two interpretations of the (multivariable) Alexander polynomial as a quantum link invariant: either by considering the quasi triangular Hopf algebra associated to at fourth roots of unity, or by considering the super Hopf algebra . In this paper, we show …
The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudo-modular Hopf algebras. Pseudo-modular Hopf algebras are a class of Z_2-graded ribbon Hopf algebras that generalise the concept of a modular H…
The paper generalizes Kuperberg invariants using twisted Drinfeld doubles.
We construct a Hopf action, with an invariant trace, of a bicrossed product Hopf algebra $\cH=\big( \cU(\Fg_1) \acr \cR(G_2) \big)^{\cop}$ constructed from a matched pair of Lie groups and , on a convolution algebra $\cA=C_c^{\ify}(G_1)\rtimes G_2^δ$. We give an explicit way to construct Hopf cyclic cohomolo…
M. Hennings and G. Kuperberg defined quantum invariants Z_{Henn} and Z_{Kup} of closed oriented 3-manifolds based on certain Hopf algebras, respectively. We prove that |Z_{Kup}|=|Z_{Henn}|^2 for lens spaces when both invariants are based on factorizable finite dimensional ribbon Hopf algebras.
The ambient framed bordism class of the connecting manifold of two consecutive critical points of a Morse-Smale function is estimated by means of a certain Hopf invariant. Applications include new examples of non-smoothable Poincare duality spaces as well as an extension of the Morse complex.
New knot polynomials derived from Nichols algebras and braided Hopf algebras.
Invariant of 3-manifolds using Hopf algebra elements.
Hennings and Kuperberg defined quantum invariants and for closed oriented -manifolds based on certain Hopf algebras, respectively. When the Hopf algebras are semisimple, it is shown that . In this paper, we present a new proof of this equality.
Researchers compute invariants for knots and links in lens spaces using large N and k limits.
New method produces positive colored superpolynomials from four-point functions.