Related papers: An invariant of tangle cobordisms
We prove several congruences for trinomial coefficients.
We consider the cobordism ring of involutions of a field of characteristic not two, whose elements are formal differences of classes of smooth projective varieties equipped with an involution, and relations arise from equivariant K-theory…
The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence…
This is a research announcement of the theory of orbifold quantum cohomology.
Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…
In this note we use techniques in the topology of 2-complexes to recast some tools that have arisen in the study of planar tiling questions. With spherical pictures we show that the tile counting group associated to a set $T$ of tiles and a…
We study the quandle counting invariant for a certain family of finite quandles with trivial orbit subquandles. We show how these invariants determine the linking number of classical two-component links up to sign.
We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.
State-sum invariants for knotted curves and surfaces using quandle cohomology were introduced by Laurel Langford and the authors in math.GT/9903135 In this paper we present methods to compute the invariants and sample computations. Computer…
We study exact Lagrangian cobordisms between exact Lagrangians in a cotangent bundle in the sense of Arnol'd, using microlocal theory of sheaves. We construct a sheaf quantization for an exact Lagrangian cobordism between Lagrangians with…
We prove a conjecture about the concordance invariant $\vartheta$, defined in a recent paper by Lewark and Zibrowius. This result simplifies the relation between $\vartheta$ and Rasmussen's $s$-invariant. The proof relies on Bar-Natan's…
We introduce a new invariant of tangles along with an algebraic framework in which to understand it. We claim that the invariant contains the classical Alexander polynomial of knots and its multivariable extension to links. We argue that of…
In this note, we give an exposition of the construction of Seiberg-Witten invariants.
A new tautological equation of $\Mbar_{3,1}$ in codimension 3 is derived and proved, using the invariance condition explained in earlier works.
We prove a result on the existence of linear forms of a given Diophantine type.
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
We investigate the algebras of invariants and the properties of the quotient morphism by an action of a finite group scheme in terms of stabilizers of points.
We prove the Shafarevich conjecture for varieties with globally generated cotangent bundle, subject to mild numerical conditions.
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
The number of colorings of a knot diagram by a quandle has been shown to be a knot invariant by CJKLS using quandle cohomology methods. In a previous paper by the second named author, the CJKLS invariant was refined and, in particular, it…