The Cohomologies of the Iwasawa Manifold and of Its Small Deformations
By Daniele Angella. 2012
88 citations recorded by the source corpus.
We prove that, for some classes of complex nilmanifolds, the Bott–Chern cohomology is completely determined by the Lie algebra associated with the nilmanifold with the induced complex structure. We use these tools to compute the Bott–Chern and Aeppli cohomologies of the Iwasawa manifold and of its small deformations, completing the computations by M. Schweitzer (arXiv:0709.3528v1 [math.AG]).
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3a434d8c547a19112386510b4e6772034638e450
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Bott–Chern cohomology of solvmanifolds (2012, unknown): “Whenever the nilmanifold is endowed with a suitable left-invariant complex structure, also the Dolbeault cohomology, [61, 25, 22, 59, 60], and the Bott-Chern cohomology, [4], can be computed by means of just left-invariant forms.”
- On the structure of double complexes (2018, background): “nctor from double complexes to vector spaces which sends squares and even-length zigzags of length <2rto the zero vector space. In particular, one immediately recovers the following fact (see also [4], [7], for previous special cases): Corollary 13. An E 1-isomorphism induces an isomorphism in Bo”