# Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary

@article{joyce2004DeformationsOA, title={Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary}, author={dominic. joyce and Sema Salur}, journal={Geometry \& Topology}, year={2004}, volume={9}, pages={1115-1146} }

McLean proved that the moduli space of coassociative deformations of a compact coassociative 4-submanifold C in a G_2-manifold (M,phi,g) is a smooth manifold of dimension equal to b^2_+(C). In this paper, we show that the moduli space of coassociative deformations of a noncompact, asymptotically cylindrical coassociative 4-fold C in an asymptotically cylindrical G_2-manifold (M,phi,g) is also a smooth manifold. Its dimension is the dimension of the positive subspace of the image of H^2_cs(C,R…

## 32 Citations

### Deformations of Asymptotically Cylindrical Coassociative Submanifolds with Moving Boundary

- Mathematics
- 2005

. In an earlier paper, [5], we proved that given an asymptotically cylindrical G 2 -manifold M with a Calabi–Yau boundary X , the moduli space of coassociative deformations of an asymptotically…

### Deformation theory of asymptotically conical coassociative 4‐folds

- Mathematics
- 2009

Suppose that a coassociative 4‐fold N in ℝ7 is asymptotically conical (AC) to a cone C with rate λ < 1. If λ ∈ [−2, 1) is generic, then we show that the moduli space of coassociative deformations of…

### Deformations of asymptotically cylindrical special Lagrangian submanifolds Sema Salur

- Mathematics
- 2010

Given an asymptotically cylindrical special Lagrangian submanifold L with fixed boundary in an asymptotically cylindrical Calabi-Yau 3-fold X, we determine conditions on a decay rate γ which make the…

### Deformations of Conically Singular Cayley Submanifolds

- MathematicsThe Journal of Geometric Analysis
- 2018

In this article, we study the deformation theory of conically singular Cayley submanifolds. In particular, we prove a result on the expected dimension of a moduli space of Cayley deformations of a…

### Deformations of Conically Singular Cayley Submanifolds

- MathematicsThe Journal of Geometric Analysis
- 2018

In this article, we study the deformation theory of conically singular Cayley submanifolds. In particular, we prove a result on the expected dimension of a moduli space of Cayley deformations of a…

### Deformations of Compact Cayley Submanifolds with Boundary

- Mathematics
- 2014

Let M be an 8-manifold with a Spin(7)-structure. We first show that closed Cayley submanifolds of M form a smooth moduli space for a generic Spin(7)-structure. Then we study the deformations of a…

### Deformations of Asymptotically Cylindrical Special Lagrangian Submanifolds with Fixed Boundary

- Mathematics
- 2009

Given an asymptotically cylindrical special Lagrangian submanifold L in an asymptotically cylindrical Calabi-Yau 3-fold X, we determine conditions on a decay rate γ which make the moduli space of…

### Deformations of Asymptotically Cylindrical Special Lagrangian Submanifolds with Moving Boundary

- Mathematics
- 2009

Given an asymptotically cylindrical special Lagrangian submanifold L in an asymptotically cylindrical Calabi-Yau 3-fold X, we determine conditions on a decay rate gamma which make the moduli space of…

### Coassociative K3 fibrations of compact G_2-manifolds

- Mathematics
- 2005

A class of examples of Riemannian metrics with holonomy G_2 on compact 7-manifolds was constructed by the author in arXiv:math.DG/0012189 and later in a joint work with N.-H. Lee in arXiv:0810.0957,…

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