Related papers: The simplest Exotic Invariant (E3)
Here we present the simple example of an Exotic Invariant with just two chiral electron supermultiplets E and P. In this example we include a mass term, and that means that there is a constraint on the Exotic Invariant. The constraint is…
We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.
This is a survey article on finite type invariants of 3-manifolds written for the Encyclopedia of Mathematical Physics to be published by Elsevier.
In this note, we give an exposition of the construction of Seiberg-Witten invariants.
In this article, we construct infinitley many simply connected, nonsymplectic and pairwise nondiffeomorphic 4-manifolds starting from E(n) and applying the sequence of knot surgery, ordinary blowups and rational blowdown. We also compute…
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…
Simple formulas are given for generating Chern-Simons basic invariant polynomials by repeated exterior differentiation for n-dimensional differentiable manifolds having a general linear connection.
In this short note, we provide an elementary complex analytic method for converting known real integrals into numerous strange and interesting looking real integrals.
This is a revised version (replacing an older one) with typos fixed and the introduction expanded.
This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics
We use a simple description of the outer automorphism of S_6 to cleanly describe the invariant theory of six points in P^1, P^2, and P^3.
The purpose of this article is twofold. First we outline a general construction scheme for producing simply-connected minimal symplectic 4-manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain…
We provide an algebraic framework to compute smallest enclosing and smallest circumscribing cylinders of simplices in Euclidean space $\E^n$. Explicitly, the computation of a smallest enclosing cylinder in $\mathbb{E}^3$ is reduced to the…
A class of spiral minimal surfaces in E^3 is constructed using a symmetry reduction. The new surfaces are invariant with respect to the composition of rotation and dilatation. The solutions are obtained in closed form %through the Legendre…
This article intends to provide an introduction to the construction of small exotic 4-manifolds. Some of the necessary background is covered. An exposition is given of J. Park's construction in arXiv:math.GT/0311395 of an exotic…
In this article, we construct the first example of a simply connected minimal symplectic 4-manifold homeomorphic but not diffeomorphic to 3CP^2#7CP^2b. We also construct the first exotic symplectic structure on CP^2#5CP^2b.
The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.
We construct invariants of four-dimensional piecewise-linear manifolds, represented as simplicial complexes, with respect to rebuildings that transform a cluster of three 4-simplices having a common two-dimensional face in a different…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
To give a parametrization of the Diophantine equation $A^{3}+B^{3}=C^{3}+D^{3}$ in terms of integral binary quadratic forms in a constructive way.