INFRA-SOLVMANIFOLDS OF Sol1₄
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The purpose of this paper is to classify all compact manifolds modeled on the 4-dimensional solvable Lie group Sol1₄, and more gener- ally, the crystallographic groups of Sol1₄. The maximal compact subgroup of Isom(Sol1₄) is D4 = Z4 ⋊ Z2. We shall exhibit an infra-solvmanifold of Sol1₄ whose holonomy is D4. This implies that all possible holonomy groups do occur; the trivial group, Z2 (5 families), Z4, Z2×Z2 (5 families), and Z4 ⋊ Z2 (2 families).
Abstract
The purpose of this paper is to classify all compact manifolds modeled on the 4-dimensional solvable Lie group Sol1₄, and more gener- ally, the crystallographic groups of Sol1₄. The maximal compact subgroup of Isom(Sol1₄) is D4 = Z4 ⋊ Z2. We shall exhibit an infra-solvmanifold of Sol1₄ whose holonomy is D4. This implies that all possible holonomy groups do occur; the trivial group, Z2 (5 families), Z4, Z2×Z2 (5 families), and Z4 ⋊ Z2 (2 families).
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