# Monopoles and Three-Manifolds

@inproceedings{Kronheimer2008MonopolesAT, title={Monopoles and Three-Manifolds}, author={Peter B. Kronheimer and Tomasz S. Mrowka}, year={2008} }

Preface 1. Outlines 2. The Seiberg-Witten equations and compactness 3. Hilbert manifolds and perturbations 4. Moduli spaces and transversality 5. Compactness and gluing 6. Floer homology 7. Cobordisms and invariance 8. Non-exact perturbations 9. Calculations 10. Further developments References Glossary of notation Index.

#### Figures from this paper

#### 324 Citations

AND CIPRIAN MANOLESCU in the sense

- 2014

Given a three-manifold with b1 = 1 and a nontorsion spin c structure, we use finite dimensional approximation to construct from the Seiberg-Witten equations two invariants in the form of a periodic… Expand

The Seiberg–Witten equations and the Weinstein conjecture

- Mathematics
- 2006

Let M denote a compact, oriented 3–dimensional manifold and let a denote a contact 1–form on M; thus a∧da is nowhere zero. This article proves that the vector field that generates the kernel of da… Expand

Hyperbolic four-manifolds with vanishing
Seiberg-Witten invariants

- Mathematics
- 2018

We show the existence of hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants, addressing a conjecture of Claude LeBrun. This is achieved by showing, using results in geometric and… Expand

Equivariant Floer theory and double covers of three-manifolds.

- Mathematics
- 2019

Inspired by Kronheimer and Mrowka's approach to monopole Floer homology, we develop a model for $\mathbb{Z}/2$-equivariant symplectic Floer theory using equivariant almost complex structures, which… Expand

Lectures on monopole Floer homology

- Mathematics
- 2016

These lecture notes are a friendly introduction to monopole Floer homology. We discuss the relevant differential geometry and Morse theory involved in the definition. After developing the relation… Expand

Superconformal simple type and Witten's conjecture

- Mathematics, Physics
- Advances in Mathematics
- 2019

Abstract Let X be a smooth, closed, connected, orientable four-manifold with b 1 ( X ) = 0 and b + ( X ) ≥ 3 and odd. We show that if X has Seiberg–Witten simple type, then the SO ( 3 ) -monopole… Expand

Unfolded Seiberg-Witten Floer spectra, II: Relative invariants and the gluing theorem

- Mathematics
- 2018

We use the construction of unfolded Seiberg-Witten Floer spectra of general 3-manifolds defined in our previous paper to extend the notion of relative Bauer-Furuta invariants to general 4-manifolds… Expand

Embedded contact homology and Seiberg-Witten Floer cohomology I

- Mathematics
- 2008

This is the first of five papers that construct an isomorphism between the embedded contact homology and Seiberg-Witten Floer cohomology of a compact 3-manifold with a given contact 1-form. This… Expand

Seiberg-Witten equation on a manifold with rank-2 foliation

- Mathematics
- 2019

Let $M$ be a closed oriented $4$-manifold admitting a rank-$2$ oriented foliation with a metric of leafwise positive scalar curvature. If $b^+>1$, then we will show that the Seiberg-Witten invariant… Expand

Floer theory and its topological applications

- Mathematics, Physics
- 2014

We survey the different versions of Floer homology that can be associated to three-manifolds. We also discuss their applications, particularly to questions about surgery, homology cobordism, and… Expand

#### References

Review : Monopoles and three - manifolds by Peter Kronheimer and Tomasz Mrowka ( PDF )

- 2009