Related papers: The simplest Exotic Invariant (E3)
Following an overview of the relevant theory, we construct several explicit examples of height-3 K3 spectra.
We give an explicit expression for the primitive E8-invariant tensor with eight symmetric indices. The result is presented in a manifestly Spin(16)/Z2-covariant notation.
We construct the first examples of what we call fake ES-irreducible components; Definition 2.8. In our way to do so, we classify the automorphism groups of smooth plane sextics that only have automorphisms of order 3 or less; Theorems 2.1,…
The construction of supersymmetric invariant actions on a spacetime manifold with a boundary is carried out using the "ectoplasm" formalism for the construction of closed forms in superspace. Non-trivial actions are obtained from the…
We describe a collection of constructions which illustrate a panoply of ``exotic'' smooth 4-manifolds.
We show that the points that converge to infinity under iteration of the exponential map form a connected subset of the complex plane.
In this note we provide a direct approach to the most basic operator in this theory namely the exterior derivative. The crucial ingredient is a calculus lemma based on determinants. We maintain the view that in a first course at least this…
We introduce the simple extension complexity of a polytope P as the smallest number of facets of any simple (i.e., non-degenerate in the sense of linear programming) polytope which can be projected onto P. We devise a combinatorial method…
An elementary approach to the construction of Coxeter group representations is presented.
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
This invited contribution summarizes some of the more important aspects of exotics. We review theoretical expectations for exotic and nonexotic hybrid mesons, and briefly discuss the leading experimental candidate for an exotic, the…
The present work pursues the aim to draw attention to unique possibilities of the skew-symmetric differential forms. At present the theory of skew-symmetric exterior differential forms that possess invariant properties has been developed.…
Examples of nonformal simply connected symplectic manifolds are constructed.
Let $M$ be $\CP#2\CPb$, $3\CP#4\CPb$ or $(2n-1)\CP#2n\CPb$ for any integer $n\geq 3$. We construct an irreducible symplectic 4-manifold homeomorphic to $M$ and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic…
We give a simple combinatoric proof of an exponential upper bound on the number of distinct 3-manifolds that can be constructed by successively identifying nearest neighbour pairs of triangles in the boundary of a simplicial 3-ball and show…
An expository survey article on Heegaard splittings
We construct a number of topologically trivial but smoothly non-trivial families of embeddings of 3-manifolds in 4-manifolds. These include embeddings of homology spheres in $S^4$ that are not isotopic but have diffeomorphic complements,…
A novel family of integrable third order maps is presented. Each map possesses, by construction, a pair of rational invariants and a commuting map from the same class. The 3-dimensional invariant curve is parametrized, in general, by an…
In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…
In a recent paper, Park constructs certain exotic simply-connected four-manifolds with small Euler characteristics. Our aim here is to prove that the four-manifolds in his constructions are minimal.