Minimal models, formality and hard Lefschetz properties of solvmanifolds with local systems

By H. Kasuya. 2010

52 citations recorded by the source corpus.

For a simply connected solvable Lie group G with a cocompact discrete subgroup {\Gamma}, we consider the space of differential forms on the solvmanifold G/{\Gamma} with values in certain flat bundle so that this space has a structure of a differential graded algebra(DGA). We construct Sullivan's minimal model of this DGA. This result is an extension of Nomizu's theorem for ordinary coefficients in the nilpotent case. By using this result, we refine Hasegawa's result of formality of nilmanifolds and Benson-Gordon's result of hard Lefschetz properties of nilmanifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ba2e53a84d1f39f5025b61ad44d4e557cb6425f6

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In Geometry and Topology

1. Daniele Angella
2. H. Kasuya
3. J. Stelzig

In Mathematical Physics

1. Daniele Angella
2. H. Kasuya
3. J. Stelzig

Citations in the corpus

• Bott–Chern cohomology of solvmanifolds (2012, result): “ovided in [28, Corollary 4.2]. The de Rham cohomology of solvmanifolds has been studied by several authors, e.g. A. Hattori [38], G. D. Mostow [54], S. Console and A. Fino [24], and the second author [40, 44]. Several results concerning the Dolbeault cohomology have been proven by the second author,”