CLASSIFICATION OF 6-DIMENSIONAL SPLITTABLE FLAT SOLVMANIFOLDS

ALEJANDRO TOLCACHIER

MANUSCRIPTA MATHEMATICA

SPRINGER

Lugar: Berlin; Año: 2021

0025-2611

A flat solvmanifold is a compact quotient 􀀀G where G is a simply-connectedsolvable Lie group endowed with a flat left invariant metric and 􀀀 is a lattice of G. Anysuch Lie group can be written as G = RknRm with Rm the nilradical. In this article wefocus on 6-dimensional splittable flat solvmanifolds, which are obtained quotienting G bya lattice 􀀀 that can be decomposed as 􀀀 = 􀀀1 n 􀀀2, where 􀀀1 and 􀀀2 are lattices of Rkand Rm, respectively. We analyze the relation between these lattices and the conjugacyclasses of finite abelian subgroups of GL(n,Z), which is known up to n 6. From thiswe obtain the classification of 6-dimensional splittable flat solvmanifolds.