Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0411116

Deformation Theory of Asymptotically Conical Coassociative 4-folds

Jason Lotay
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study coassociative 4-folds N in R^7 which are asymptotically conical to a cone C with rate lambda<1. If lambda is in the interval [-2,1) and generic, we show that the moduli space of coassociative deformations of N which are also asymptotically conical to C with rate lambda is a smooth manifold, and we calculate its dimension. If lambda<-2 and generic, we show that the moduli space is locally homeomorphic to the kernel of a smooth map between smooth manifolds, and we give a lower bound for its expected dimension. We also derive a test for when N will be planar if lambda<-2 and we discuss examples of asymptotically conical coassociative 4-folds.

Explore related subjects

math.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jason Lotay. 2009-10-26. Deformation Theory of Asymptotically Conical Coassociative 4-folds. https://doi.org/10.1112/plms%2Fpdp006

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Cohomology of Lie algebroids over topological ringed spaces

We consider Lie algebroids over a topological ringed space as quasicoherent sheaves of Lie-Rinehart algebras. We express hypercohomology for a locally free Lie algebroid (not necessarily of finite rank) as a derived functor, and simplify it via Čech cohomology. Furthermore, we define the Hochschild hypercohomology of a sheaf of generalized bialgebras (using a derived functor) and study the cases of the universal enveloping algebroid and of the jet algebroid of a Lie algebroid. In the sequel, we present a version of Hochschild-Kostant-Rosenberg theorem for a locally free Lie algebroid, as well as its dual version.

math.DG↗
arXiv2026

Family index for Fredholm extensions of semi-Fredholm operators

This paper is devoted to an abstract analogue of elliptic boundary value problems, namely, Fredholm realizations of semi-Fredholm operators in a Hilbert space. Such a realization is determined by an abstract boundary condition, which is a subspace in the space of abstract boundary values. We find the $K^0$ index of a family of such abstract boundary value problems, or the $K^1$ index in the self-adjoint case, in terms of the corresponding family of abstract boundary conditions. Our approach is based on passing from a Fredholm operator to its graph. The graph forms a Fredholm pair with the horizontal subspace, and we prove the index formula by deforming the horizontal subspace instead of the operator.

math.DG↗
arXiv2026

Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space

We study the equivalence classes of slice-regular functions $f:Ω\to\mathbb{H}$ on a symmetric slice domain $Ω$, and of their subclass made of polynomial slice-regular functions, with respect to the natural action of $\mathrm{PGL}(2,\mathbb{H})$ and its subgroups, by employing the twistor construction. In particular, we characterize slice--regular functions whose twistor lift is planar and belongs to a given orbit, and we find normal classes of slice-regular polynomials with respect to the action of a parabolic subgroup of $\mathrm{GL}(2,\mathbb{H})$.

math.DG↗