Related papers: The simplest Exotic Invariant (E3)

In a small simply-connected closed 4-manifold, we construct infinitely many pairs of exotic codimension-$1$ submanifolds with diffeomorphic complements that remain exotic after any number of stabilizations by $ S^2 \times S^2$. We also give…

This is a survey of known algorithms in algebraic topology with a focus on finite simplicial complexes and, in particular, simplicial manifolds. Wherever possible an elementary approach is chosen. This way the text may also serve as a…

In this paper we use a design theoretical approach to construct new, previously unknown complex Hadamard matrices. Our methods generalize and extend the earlier results of de la Harpe--Jones and Munemasa--Watatani and offer a theoretical…

We construct several new families of Fano varieties of K3 type. We give a geometrical explanation of the K3 structure and we link some of them to projective families of irreducible holomorphic symplectic manifolds.

These introductory lectures show how to define finite type invariants of links and 3-manifolds by counting graph configurations in 3-manifolds, following ideas of Witten and Kontsevich. The linking number is the simplest finite type…

In this paper we present three simple applications of probability and highlight and discuss their paradoxical flavour.

We construct an infinite family of simply connected, pairwise nondiffeomorphic 4-manifolds, all homeomorphic to 3CP^2 blown up at 9 points.

We introduce a numerical isomorphism invariant p(T) for any triangulation T of S^3. Although its definition is purely topological (inspired by the bridge number of knots), p(T) reflects the geometric properties of T. Specifically, if T is…

We associate an integer to any simple polytope and we study its properties.

Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.

We study the random composition of a small family of O(n^3) simple permutations on {0,1}^n. Specifically we ask how many randomly selected simple permutations need be composed to yield a permutation that is close to k-wise independent. We…

This article present a new, direct and simple formula for constructing Mignotte sequences.

To solve MHD problems within the framework of the theory of two-scale mean fields, it is important to study the invariants of magnetic lines. Such invariants are constructed on the basis of invariants of classical links, which must satisfy…

We construct a simply connected $2-$complex $C$ embeddable in $3-$space such that for any embedding of $C$ in $\mathbb S^3$, any edge contraction forms a minor of the $2-$complex not embeddable in $3-$space. We achieve this by proving that…

First, we establish an abstract ergodic result on $\mR^d$. Classical ergodic results on $\mR^d$ require that the process is irreducible, we weaken it to some weak form of irreducibility in this article. The main method used in this article…

We exploit various inclusions of algebraic groups to give a new construction of groups of type E8, determine the Killing forms of the resulting E8's, and define an invariant of central simple algebras of degree 16 with orthogonal involution…

An invariant of orientable 3-manifolds is defined by taking the minimum $n$ such that a given 3-manifold embeds in the connected sum of $n$ copies of $S^2 \times S^2$, and we call this $n$ the embedding number of the 3-manifold. We give…

We construct the first exotic $\mathbb C \mathbb P^2 \# 4 \overline{\mathbb C \mathbb P^2}$ by means of rational blowdowns. Similarly, we construct the first exotic $3\mathbb C \mathbb P^2 \# b^- \overline{\mathbb C \mathbb P^2}$ for…

In this paper we construct and classify Lagrangian T^3-fibrations on non compact symplectic manifolds with singular fibres of prescribed topological type. This contributes to the understanding of the structure of the singular fibres that…

In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of…