Related papers: The quadratic linking degree
This article serves a two-fold purpose. On the one hand, it is a survey about the classification of finite-dimensional pointed Hopf algebras with abelian coradical, whose final step is the computation of the liftings or deformations of…
We develop a general homological approach to presentations of connected graded associative algebras, and apply it to the loop homology of moment-angle complexes $Z_K$ that correspond to flag simplicial complexes $K$. For arbitrary…
We define half grid diagrams and prove every link is half grid presentable by constructing a canonical half grid pair (which gives rise to a grid diagram of some special type) associated with an element in the oriented Thompson group. We…
The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index class…
We give a characterization of symplectic quadratic Lie algebras that their Lie algebra of inner derivations has an invertible derivation. A family of symplectic quadratic Lie algebras is introduced to illustrate this situation. Finally, we…
In this paper we study the problem of determining the homology groups of a quotient of a topological space by an action of a group. The method is to represent the original topological space as a homotopy limit of a diagram, and then act…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
Two links are called link-homotopic if they are transformed to each other by a sequence of self-crossing changes and ambient isotopies. The notion of link-homotopy is generalized to spatial graphs and it is called component-homotopy. The…
We prove the following "linkage" theorem: two p-regular graphs of the same genus can be obtained from one another by a finite alternating sequence of one-edge-contractions; moreover this preserves 3-edge-connectivity. We use the linkage…
The linking number of an oriented two-component link is an invariant indicating how intertwined the two components are. Tuler proved that the linking number of a two-component rational $\frac{p}{q}$-link is $$\sum^{\frac{|p|}{2}}_{k=1}…
We analyse topological orbifold conformal field theories on the symmetric product of a complex surface M. By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by…
This is a foundation for algebraic geometry, developed internal to the Zariski topos, building on the work of Kock and Blechschmidt. The Zariski topos consists of sheaves on the site opposite to the category of finitely presented algebras…
We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as well as to say when some thin groups cannot be conjugate to…
We construct a 2-variable link polynomial, called $W_L$, for classical links by considering simultaneously the Kauffman state models for the Alexander and for the Jones polynomials. We conjecture that this polynomial is the product of two…
We apply the degree formula for connective $K$-theory to study rational contractions of algebraic varieties. Examples include rationally connected varieties and complete intersections.
The classical Hurwitz numbers of degree n together with the Hurwitz numbers of the seamed surfaces of degree n give rise to the Klein topological field theory. We extend this construction to the Hurwitz numbers of all degrees at once. The…
We study the class of all algebras that are isotopic to a Hurwitz algebra. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. A complete, geometrically intuitive description of the category of…
We exhibit a connection between two statistics on set partitions, the intertwining number and the depth-index. In particular, results link the intertwining number to the algebraic geometry of Borel orbits. Furthermore, by studying the…
We determine that the Chow ring (with ${\bf Q}$-coefficients) of the Hurwitz space parametrizing degree three covers of ${\bf P}^{1}$ is tautological. We also compute the rational Picard groups of auxiliary spaces of degree three maps with…
We study several different notions of algebraicity in use in stable homotopy theory and prove implications between them. The relationships between the different meanings of algebraic are unexpectedly subtle, and we illustrate this with…