# Gluing in geometric analysis via maps of Banach manifolds with corners and applications to gauge theory.

@article{Feehan2019GluingIG, title={Gluing in geometric analysis via maps of Banach manifolds with corners and applications to gauge theory.}, author={Paul M. N. Feehan and Thomas G. Leness}, journal={arXiv: Differential Geometry}, year={2019} }

We describe a new approach to the problem of constructing gluing parameterizations for open neighborhoods of boundary points of moduli spaces of anti-self-dual connections over closed four-dimensional manifolds. Our approach employs general results from differential topology for $C^1$ maps of smooth Banach manifolds with corners, providing a method that should apply to other problems in geometric analysis involving the gluing construction of solutions to nonlinear partial differential equations…

## One Citation

### Introduction to virtual Morse-Bott theory on analytic spaces, moduli spaces of SO(3) monopoles, and applications to four-manifolds.

- Mathematics
- 2020

We introduce an approach to Morse-Bott theory, called virtual Morse-Bott theory, for Hamiltonian functions of circle actions on closed, real analytic, almost Hermitian spaces. In the case of…

## References

SHOWING 1-10 OF 101 REFERENCES

### The Homotopy Type of Gauge Theoretic Moduli Spaces

- Mathematics
- 1994

In recent years Gauge theory has been perhaps the most important technique in the study of differentiable structures on four dimensional manifolds. In particular the study of the moduli spaces of…

### Smooth Four-Manifolds and Complex Surfaces

- Mathematics
- 1994

This book applies the recent techniques of gauge theory to study the smooth classification of compact complex surfaces. The study is divided into four main areas: Classical complex surface theory,…

### Equivariant collaring, tubular neighbourhood and gluing theorems for proper Lie group actions

- Mathematics
- 2007

The purpose of this paper is to prove equivariant versions of some basic theorems in differential topology for proper Lie group actions. In particular, we study how to extend equivariant isotopies…

### Properties of pseudo-holomorphic curves in symplectisations II: Embedding controls and algebraic invariants

- Mathematics
- 1995

In the following we look for conditions on a finite energy plane ũ : = (a, u) : ℂ → ℝ × M, which allow us to conclude that the projection into the manifold M, u : ℂ → M, is an embedding. For this…

### Integration theory on the zero sets of polyfold Fredholm sections

- Mathematics
- 2007

We construct an integration theory for sc-differential forms on oriented branched ep-subgroupoid for which Stokes’ theorem holds true. The construction is compatible with equivalences between…

### Properties of Pseudoholomorphic Curves in Symplectizations III: Fredholm Theory

- Mathematics
- 1999

We shall study smooth maps ũ: S → ℝ x M of finite energy defined on the punctured Riemann surface S = S\Γ and satisfying a Cauchy-Riemann type equation Tũ ∘ j = Jũ ∘ Tũ for special almost complex…

### The Riemannian geometry of the Yang-Mills moduli space

- Mathematics
- 1987

The moduli space ℳ of self-dual connections over a Riemannian 4-manifold has a natural Riemannian metric, inherited from theL2 metric on the space of connections. We give a formula for the curvature…

### Morse-Bott theory and equivariant cohomology

- Mathematics
- 1995

Critical points of functions and gradient lines between them form a cornerstone of physical thinking. In Morse theory the topology of a manifold is investigated in terms of these notions with equally…

### Sc-Smoothness, Retractions and New Models for Smooth Spaces

- Mathematics
- 2010

We survey a (nonlinear) Fredholm theory for a new class of ambient spaces called polyfolds, and develop the analytical foundations for some of the applications of the theory. The basic feature of…

### A general Fredholm theory I: A splicing-based differential geometry

- Mathematics
- 2006

This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. These spaces, in general, are locally not homeomorphic to open sets in…