On the Conjectures Regarding the 4-Point Atiyah Determinant
نویسندگان
چکیده
For the case of 4 points in Euclidean space, we present a computer aided proof of Conjectures II and III made by Atiyah and Sutcliffe regarding Atiyah’s determinant along with an elegant factorization of the square of the imaginary part of Atiyah’s determinant.
منابع مشابه
Periodicity Theorems and Conjectures in Hermitian K-theory
The purpose of this appendix to [4], is to state some periodicity theorems and conjectures in an algebraic context which are related to Bak’s work on the K-theory of forms [1]. Periodicity theorems in topological K-theory have already some history going back to Bott, Atiyah and others (see [5] for a survey). As we shall see, the analog of these theorems in a purely algebraic context uses the or...
متن کاملThe Hodge Numbers of the Moduli Spaces of Vector Bundles over a Riemann Surface
Let M(n, d) denote the moduli space of stable holomorphic vector bundles of coprime rank n and degree d over a fixed Riemann surface Σ of genus g ≥ 2. Let Λ be a fixed line bundle over Σ of degree d and let MΛ(n, d) ⊂ M(n, d) denote the space consisting of those bundles with determinant Λ. The spaces M(n, d) and MΛ(n, d) are nonsingular complex projective varieties whose geometry has been much ...
متن کاملOn a conjecture of Atiyah
In this note we explain how the computation of the spectrum of the lamplighter group from [GZ01] yields a counterexample to a strong version of the Atiyah conjectures about the range of L -Betti numbers of closed manifolds.
متن کاملمعمای واگن و تلویحات آن برای اتانازی فعال و غیر فعال
Theologians describe the difference between active and passive euthanasia as in the former, we kill hopeless patients terribly suffering from an incurable disease and in the latter, and we let them die. The present research aimed at exploring for a solution to an ethical dilemma by which the difference between foundational concepts of the two types of euthanasia can be examined. Another objecti...
متن کاملRigidity and Vanishing Theorems in K-Theory I
In this paper, we first establish a K-theory version of the equivariant family index theorem for a circle action, then use it to prove several rigidity and vanishing theorems on the equivariant K-theory level. 0 Introduction. In [W], Witten considered the indices of elliptic operators on the free loop space LM of a spin manifold M . In particular the index of the formal signature operator on th...
متن کامل