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Title: Lefschetz coincidence numbers of solvmanifolds with Mostow conditions (English)
Author: Kasuya, Hisashi
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 50
Issue: 1
Year: 2014
Pages: 27-37
Summary lang: English
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Category: math
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Summary: For any two continuous maps $f$, $g$ between two solvmanifolds of the same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence number of $f$, $g$. This result is an extension of the result of Ha, Lee and Penninckx for completely solvable case. (English)
Keyword: de Rham cohomology
Keyword: Lefschetz coincidence number
Keyword: solvmanifold
MSC: 17B55
MSC: 22E25
MSC: 53C30
MSC: 54H25
MSC: 55M20
idZBL: Zbl 06391563
idMR: MR3194766
DOI: 10.5817/AM2014-1-27
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Date available: 2014-04-04T07:40:08Z
Last updated: 2015-03-19
Stable URL: http://hdl.handle.net/10338.dmlcz/143717
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Reference: [1] Auslander, L.: An exposition of the structure of solvmanifolds. I. Algebraic theory.Bull. Amer. Math. Soc. 79 (1973), no. 2, 227–261. Zbl 0265.22016, MR 0486307, 10.1090/S0002-9904-1973-13134-9
Reference: [2] Baues, O., Klopsch, B.: Deformations and rigidity of lattices in solvable Lie groups.J. Topol. (online published). MR 3145141
Reference: [3] Console, S., Fino, A.: On the de Rham cohomology of solvmanifolds.Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 10 (2011), no. 4, 801–811. Zbl 1242.53055, MR 2932894
Reference: [4] Ha, K.Y., Lee, J.B., Penninckx, P.: Anosov theorem for coincidences on special solvmanifolds of type (R).Proc. Amer. Math. Soc. 139 (2011), no. 6, 2239–2248. MR 2775401
Reference: [5] Hattori, A.: Spectral sequence in the de Rham cohomology of fibre bundles.J. Fac. Sci. Univ. Tokyo Sect. I 8 (1960), 289–331. Zbl 0099.18003, MR 0124918
Reference: [6] Jezierski, J., Marzantowicz, W.: Homotopy methods in topological fixed and periodic points theory.Topol. Fixed Point Theory Appl., vol. 3, Springer, Dordrecht, 2006. Zbl 1085.55001, MR 2189944
Reference: [7] Kasuya, H.: The Frolicher spectral sequences of certain solvmanifolds.J. Geom. Anal. (2013), Online First. MR 3299283, 10.1007/s12220-013-9429-2
Reference: [8] Kasuya, H.: Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds.Bull. Lond. Math. Soc. 45 (2013), no. 1, 15–26. Zbl 1262.53061, MR 3033950, 10.1112/blms/bds057
Reference: [9] McCleary, J.: A user’s guide to spectral sequences.second ed., Cambridge Studies in Advanced Mathematics, Cambridge, 2001. Zbl 0959.55001, MR 1793722
Reference: [10] McCord, C. K.: Lefschetz and Nielsen coincidence numbers on nilmanifolds and solvmanifolds.Topology Appl. 75 (1997), no. 1, 81–92. Zbl 1001.55004, MR 1425386, 10.1016/S0166-8641(96)00081-8
Reference: [11] McCord, C.K., : Nielsen numbers and Lefschetz numbers on solvmanifolds.Pacific J. Math. 147 (1991), no. 1, 153–164. Zbl 0666.55002, MR 1081679, 10.2140/pjm.1991.147.153
Reference: [12] Mostow, G.D.: Cohomology of topological groups and solvmanifolds.Ann. of Math. (2) 73 (1961), 20–48. Zbl 0103.26501, MR 0125179
Reference: [13] Nomizu, K.: On the cohomology of compact homogeneous spaces of nilpotent Lie groups.Ann. of Math. (2) 59 (1954), 531–538. Zbl 0058.02202, MR 0064057, 10.2307/1969716
Reference: [14] Onishchik, A.L., Vinberg, E.B.: Lie groups and Lie algebras II.Springer, 2000. Zbl 0932.00011, MR 1756406
Reference: [15] Raghnathan, M.S.: Discrete subgroups of Lie Groups.Springer-Verlag, New York, 1972. MR 0507234
Reference: [16] Steenrod, N.: The Topology of Fibre Bundles.Princeton University Press, 1951. Zbl 0054.07103, MR 0039258
Reference: [17] Witte, D.: Superrigidity of lattices in solvable Lie groups.Invent. Math. 122 (1995), no. 1, 147–193. Zbl 0844.22015, MR 1354957, 10.1007/BF01231442
Reference: [18] Wong, P.: Reidemeister number, Hirsch rank, coincidences on polycyclic groups and solvmanifolds.J. Reine Angew. Math. 524 (2000), 185–204. Zbl 0962.55002, MR 1770607
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