# Instantons and Four-Manifolds

@inproceedings{Freed1984InstantonsAF, title={Instantons and Four-Manifolds}, author={Daniel S. Freed and Karen K. Uhlenbeck}, year={1984} }

This volume has been designed to explore the confluence of techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds. It aims to be beneficial to those graduate students or mathematical researchers who wish to understand the work of Donaldson and the applications of gauge theories to four-dimensional topology.

## 515 Citations

Lectures on Four-Manifolds and Topological Gauge Theories

- Mathematics, Physics
- 1995

I give an elementary introduction to the theory of four-manifold invariants and its relation with topological field theory. I review the recent developments in the theory of Donaldson and…

The Hamiltonian structure of Yang-Mills theories and instantons II

- Mathematics
- 1986

Abstract The formalism of constraints, reviewed in paper I, is applied to Yang-Mills theory to determine the physical phase space. This turns out to be the cotangent bundle of orbit space, the space…

PIECEWISE LINEAR STRUCTURES ON TOPOLOGICAL MANIFOLDS

- Mathematics
- 2015

This is a survey paper where we expose the Kirby--Siebenmann results on classification of PL structures on topological manifolds and, in particular, the homotopy equivalence TOP/PL=K(Z/2.3) and the…

The Smith Conjecture in dimension four and equivariant gauge theory

- Mathematics
- 1993

We study actions of a compact, not necessarily connected Lie group on a compact, oriented, definite 4-manifold. From the equivariant geometry of the one-instanton moduli space, we derive in a…

The Theta Divisor and Three-Manifold Invariants

- Mathematics
- 2000

In this paper we study an invariant for oriented three-manifolds with $b_1>0$, which is defined using Heegaard splittings and the theta divisor of a Riemann surface. The paper is divided into two…

Instantons for 4-manifolds with periodic ends and an obstruction to embeddings of 3-manifolds

- MathematicsTopology and its Applications
- 2018

Abstract We construct an obstruction to the existence of embeddings of a homology 3-sphere into a homology S 3 × S 1 under some cohomological condition. The obstruction is defined as an element in…

Gauge theory for embedded surfaces , II

- 1997

This paper is the second in a series of two, aimed at developing results about the topology of embedded surfaces Σ in a 4-manifold X using some new YangMills moduli spaces associated to such pairs…

Gauge theory for embedded surfaces, II

- Mathematics
- 1993

This paper is the second in a series of two, aimed at developing results about the topology of embedded surfaces Σ in a 4-manifold X using some new YangMills moduli spaces associated to such pairs…

Gauge Fields in Physics and Mathematics

- Physics
- 2002

Abstract The interaction between geometry, topology and physics is becoming ever more intense and fruitful and much of this interaction flows from the observation, made over two decades ago, that the…

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…