A gauge theoretic approach to Einstein 4-manifolds

Joel Fine; Kirill Krasnov; Dmitri Panov

A gauge theoretic approach to Einstein 4-manifolds

Joel Fine^*, Kirill Krasnov, Dmitri Panov

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent account of the theory in purely mathematical language. We then explain why the new approach may have important mathematical applications: the possibility of using the calculus of variations to find Einstein 4-manifolds, as well as links to symplectic topology. We also carry out some of the technical groundwork to attack these problems.

Original language	English
Pages (from-to)	293-323
Number of pages	31
Journal	New york journal of mathematics
Volume	20
Publication status	Published - Apr 2014

Keywords

Einstein manifolds
4-manifolds
gauge theory
QUATERNIONIC-KAHLER-MANIFOLDS
HYPERBOLIC GEOMETRY
RIGIDITY THEOREM
TWISTOR SPACES
CONSTANTS

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http://nyjm.albany.edu/j/2014/20-18.html

Cite this

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abstract = "This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent account of the theory in purely mathematical language. We then explain why the new approach may have important mathematical applications: the possibility of using the calculus of variations to find Einstein 4-manifolds, as well as links to symplectic topology. We also carry out some of the technical groundwork to attack these problems.",

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AU - Fine, Joel

AU - Krasnov, Kirill

AU - Panov, Dmitri

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N2 - This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent account of the theory in purely mathematical language. We then explain why the new approach may have important mathematical applications: the possibility of using the calculus of variations to find Einstein 4-manifolds, as well as links to symplectic topology. We also carry out some of the technical groundwork to attack these problems.

AB - This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent account of the theory in purely mathematical language. We then explain why the new approach may have important mathematical applications: the possibility of using the calculus of variations to find Einstein 4-manifolds, as well as links to symplectic topology. We also carry out some of the technical groundwork to attack these problems.

KW - Einstein manifolds

KW - 4-manifolds

KW - gauge theory

KW - QUATERNIONIC-KAHLER-MANIFOLDS

KW - HYPERBOLIC GEOMETRY

KW - RIGIDITY THEOREM

KW - TWISTOR SPACES

KW - CONSTANTS

M3 - Article

SN - 1076-9803

VL - 20

SP - 293

EP - 323

JO - New york journal of mathematics

JF - New york journal of mathematics

ER -

A gauge theoretic approach to Einstein 4-manifolds

Abstract

Keywords

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