Compact flat manifolds with holonomy group 𝐙 2 ⨁ 𝐙 2 (II)

J. P. Rossetti; P. A. Tirao

Rendiconti del Seminario Matematico della Università di Padova (1999)

  • Volume: 101, page 99-136
  • ISSN: 0041-8994

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Rossetti, J. P., and Tirao, P. A.. "Compact flat manifolds with holonomy group $\mathbf {Z}_2 \bigoplus \mathbf {Z}_2$ (II)." Rendiconti del Seminario Matematico della Università di Padova 101 (1999): 99-136. <http://eudml.org/doc/108496>.

@article{Rossetti1999,
author = {Rossetti, J. P., Tirao, P. A.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {fundamental group; compact flat manifold; holonomy group; Betti number},
language = {eng},
pages = {99-136},
publisher = {Seminario Matematico of the University of Padua},
title = {Compact flat manifolds with holonomy group $\mathbf \{Z\}_2 \bigoplus \mathbf \{Z\}_2$ (II)},
url = {http://eudml.org/doc/108496},
volume = {101},
year = {1999},
}

TY - JOUR
AU - Rossetti, J. P.
AU - Tirao, P. A.
TI - Compact flat manifolds with holonomy group $\mathbf {Z}_2 \bigoplus \mathbf {Z}_2$ (II)
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1999
PB - Seminario Matematico of the University of Padua
VL - 101
SP - 99
EP - 136
LA - eng
KW - fundamental group; compact flat manifold; holonomy group; Betti number
UR - http://eudml.org/doc/108496
ER -

References

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  1. [1] H. Brown - R. Bülow - J. Neub - H. Wondratschok - H. Zassenhaus, Crystallografic Groups of Four-Dimensional Space, Wiley, New York (1978). 
  2. [2] L. Charlap, Bieberbach Groups and Flat Manifolds, Springer-Verlag, New York (1986). Zbl0608.53001MR862114
  3. [3] L. Charlap, Compact Flat Manifolds: I, Ann. of Math., 81 (1965), pp. 15-30. Zbl0132.16506MR170305
  4. [4] P. Cobb, Manifolds with holonomy group Z2 ⊕ Z2 and first Betti number zero, J. Differential Geometry, 10 (1975), pp. 221-224. Zbl0349.53027
  5. [5] I. Dotti Miatello - R. Miatello, Isospectral compact flat manifolds, Duke Mathematical Journal, 68 (1992), pp. 489-498. Zbl0781.53032MR1194952
  6. [6] D. Heisler, On the cohomology of modules over the Klein group, Ph. D. Thesis, State University of New York atStony Brook (1973). 
  7. [7] H. Hiller - C. Sah, Holonomy offlat manifolds with β 1= 0, Quart. J. Math. Oxford (2), 37 (1986), pp. 177-187. Zbl0598.57014
  8. [8] P. Hindman - L. Klingler - C.J. Odenthal, On the Krull-Schmidt-Azumaya theorem for integral group rings, Comm. in Algebra, to appear. Zbl0914.20003MR1647074
  9. [9] L. Nazarova, Integral representations of the Klein's four group, Dokl. Akad. Nauk. SSSR, 140 (1961), p. 1011; English transl. in Soviet Math. Dokl., 2 (1961) p. 1304. Zbl0106.02602MR130916
  10. [10] I. Reiner, Integral representations of cyclic groups of prime order, Proc. Amer. Math. Soc., 8 (1957), pp. 142-146. Zbl0077.25103MR83493
  11. [11] I. Reiner, Failure of the Krull-Schmidt theorem for integral representations, Michigan Math. Jour., 9 (1962), pp. 225-231. Zbl0106.02504MR144942
  12. [12] J. Rossetti - P. Tirao, Compact Flat Manifolds with Holonomy Group Z2⊕Z2, Proc. Amer. Math Soc., 124 (1996), pp. 2491-2499. Zbl0864.53027
  13. [13] H. Zassenhaus, Uber einen Algorithmus zur Bestimmung der Raumgruppen, Comment. Math. Helvetici, 21 (1948), pp. 117-141. Zbl0030.00902MR24424

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