Geodesic
On the holomorphic torus-Bott tower of aspherical manifolds
Informatics and Automation, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 275-290.

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We introduce a notion of holomorphic torus-Bott tower which is an iterated holomorphic Seifert fiber space with fiber a complex torus. This is thought of as a holomorphic version of a real Bott tower. The top space of the holomorphic torus-Bott tower is called a holomorphic torus-Bott manifold. We discuss the structure of holomorphic torus-Bott manifolds and particularly the holomorphic rigidity of holomorphic torus-Bott manifolds. 
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Yoshinobu Kamishima; Mayumi Nakayama. On the holomorphic torus-Bott tower of aspherical manifolds. Informatics and Automation, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 275-290. http://geodesic.mathdoc.fr/item/TRSPY_2014_286_a14/

[1] Baues O., “Infra-solvmanifolds and rigidity of subgroups in solvable linear algebraic groups”, Topology, 43:4 (2004), 903–924 | DOI | MR | Zbl

[2] Baues O., Cortés V., “Aspherical Kähler manifolds with solvable fundamental group”, Geom. dedicata, 122 (2006), 215–229 | DOI | MR | Zbl

[3] Carrell J.B., “Holomorphically injective complex toral actions”, Proc. 2nd Conf. on Compact Transformation Groups, Part II, Lect. Notes Math., 299, Springer, Berlin, 1972, 205–236 | DOI | MR

[4] Conner P.E., Raymond F., “Actions of compact Lie groups on aspherical manifolds”, Topology of manifolds, Proc. Univ. Georgia, 1969, Markham, Chicago, 1971, 227–264 | MR

[5] Conner P.E., Raymond F., “Injective operations of the toral groups”, Topology., 10:4 (1971), 283–296 | DOI | MR | Zbl

[6] Conner P.E., Raymond F., “Holomorphic Seifert fibering”, Proc. 2nd Conf. on Compact Transformation Groups, Part II, Lect. Notes Math., 299, Springer, Berlin, 1972, 124–204 | DOI | MR

[7] Hasegawa K., “A note on compact solvmanifolds with Kähler structures”, Osaka J. Math., 43 (2006), 131–135 | MR | Zbl

[8] Hasegawa K., Kamishima Y., Compact homogeneous locally conformally Kähler manifolds, E-print, 2013, arXiv: 1312.2202 [math.CV]

[9] Hirzebruch F., Topological methods in algebraic geometry, Grundl. Math. Wiss., 131, Springer, Berlin, 1966 | MR

[10] Kamishima Y., Lee K.B., Raymond F., “The Seifert construction and its applications to infranilmanifolds”, Q. J. Math. Oxford. Ser. 2, 34 (1983), 433–452 | DOI | MR | Zbl

[11] Kamishima Y., Nakayama M., “Topology of nilBott tower of aspherical manifolds” (to appear)

[12] Kamishima Y., Nakayama M., Torus actions and the Halperin–Carlsson conjecture, E-print, 2012, arXiv: 1206.4790v1 [math.GT]

[13] Kamishima Y., Tanaka A., “On complex contact similarity manifolds”, J. Math. Res., 5:4 (2013), 1–10 | DOI

[14] Lee K.B., Raymond F., Seifert fiberings, Math. Surv. Monogr., 166, Amer. Math. Soc., Providence, RI, 2010 | DOI | MR | Zbl

[15] Murakami S., “Sur certains espaces fibrés principaux holomorphes admettant des connexions holomorphes”, Osaka Math. J., 11 (1959), 43–62 | MR | Zbl

[16] Nakayama M., “On the $S^1$-fibred nilBott tower”, Osaka J. Math., 51 (2014), 67–89, arXiv: 1110.1164 [math.AT] | MR | Zbl

[17] Rollenske S., “Geometry of nilmanifolds with left-invariant complex structure and deformations in the large”, Proc. London Math. Soc. Ser. 3, 99:2 (2009), 425–460 | DOI | MR | Zbl

[18] Salamon S.M., “Complex structures on nilpotent Lie algebras”, J. Pure Appl. Algebra, 157 (2001), 311–333 | DOI | MR | Zbl

[19] Ugarte L., “Hermitian structures on six-dimensional nilmanifolds”, Transform. Groups, 12:1 (2007), 175–202 | DOI | MR | Zbl