In order to put the Gowdy class of spacetimes into context, it is natural to start by discussing the role of symmetry in general relativity. We shall not discuss it here in all generality, but will restrict our attention to the four-dimensional cosmological case.

2.1 Symmetry in cosmology

2.1.1 Symmetry via the Lie algebra

2.1.2 Symmetry via Lie group actions on the spacetime

2.1.3 Symmetry via the initial value formulation

2.1.4 Cosmological symmetry hierarchy

2.1.5 Limitations, different perspectives

2.1.6 Present status, hierarchy

2.2 Definition of the Gowdy class

2.2.1 Twist constants, two-surface orthogonality

2.2.2 Essential characterizing conditions

2.2.3 Technical definition

2.3 Coordinate systems

2.3.1 Coordinate systems, T^{3}-Gowdy

2.3.2 Working definition, T^{3}-Gowdy

2.3.3 Coordinate system, S^{3} and S^{2} × S^{1}

2.4 The polarized subcase

2.1.1 Symmetry via the Lie algebra

2.1.2 Symmetry via Lie group actions on the spacetime

2.1.3 Symmetry via the initial value formulation

2.1.4 Cosmological symmetry hierarchy

2.1.5 Limitations, different perspectives

2.1.6 Present status, hierarchy

2.2 Definition of the Gowdy class

2.2.1 Twist constants, two-surface orthogonality

2.2.2 Essential characterizing conditions

2.2.3 Technical definition

2.3 Coordinate systems

2.3.1 Coordinate systems, T

2.3.2 Working definition, T

2.3.3 Coordinate system, S

2.4 The polarized subcase

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