Abstract
This is the first of a three parts paper providing full details for our previous announcement in Prepublications Orsay 2007-16, arXiv.org/abs/0711.3579. Here we prove the results stated in the title.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brick S., Mihalik M.: The QSF property for groups and spaces. Math. Z. 220, 207–217 (1995)
Funar, L., Gadgil, S.: On the geometric simple connectivity of open manifolds. IMRN (24), 1193–1242 (2004)
Funar L., Otera D.: On the WGSC and QSF tameness conditions for finitely presented groups. Groups Geom. Dyn. 4, 549–596 (2010)
Gersten S., Stallings J.: Casson’s idea about 3-manifolds whose universal cover is R 3. Int. J. Algebra Comput. 1, 395–406 (1991)
Otera, D.: Asymptotic topology of groups, connectivity at infinity and geometric simple connectivity. Ph. Thesis Université Paris Sud-Orsay (2006)
Otera, D., Poénaru, V.: “Easy” Representations and the QSF property for groups (to appear in the Bull. of the Belgian Math. Soc.– Simon Stevin) (2011)
Otera, D., Poénaru, V., Tanasi, C.: On geometric simple connectivity. Bull. Math. Soc. Sci. Math. Roumanie Nouvelle série 53(101)(2), 157–176 (2010)
Poénaru V.: On the equivalence relation forced by the singularities of a non degenerate simplicial map. Duke Math. J. 63(2), 421–429 (1991)
Poénaru V.: Killing handles of index one stably and \({\pi_1^{\infty} }\) . Duke Math. J. 63(2), 431–447 (1991)
Poénaru V.: The collapsible pseudo-spine representation theorem. Topology 31(3), 625–636 (1992)
Poénaru V.: Almost convex groups, Lipschitz combing, and \({\pi_1^{\infty} }\) for universal covering spaces of 3-manifolds. J. Diff. Geom. 35, 103–130 (1992)
Poénaru, V.: Geometric simple connectivity in four-dimensional differential topology, Part A. IHÉS Prépublications M/10/45 (2001). http://www.ihes.fr/PREPRINTS-M01/Resu/resu-M01-45.htm
Poénaru V.: Geometric simple connectivity and low-dimensional topology. Proc. Steklov Inst. Math. 247, 195–208 (2004)
Poénaru, V.: On the 3-dimensional Poincaré Conjecture and the 4-dimensional Smooth Schoenflies Problem. Préprint Univ. Paris-Sud Orsay 2006-25 (2006), ArXiv.org/abs/math.GT/0612554
Poénaru, V.: Discrete symmetry with compact fundamental domain, and geometric simple connectivity. Préprint Univ. Paris-Sud Orsay 2007-16 (2007). http://ArXiv.org/als/0711.3579
Poénaru V., Tanasi C.: Some remarks on geometric simple connectivity. Acta Math. Hungarica 81, 1–12 (1998)
Poénaru, V., Tanasi, C.: Equivariant, almost-arborescent representations of open simply-connected 3-manifolds; a finiteness result. Memoirs of the AMS 169(800) (2004)
Poénaru V., Tanasi C.: Representations of the whitehead manifold \({{\rm Wh}^3}\) and Julia sets. Ann. Toulouse IV(3), 665–694 (1995)
Stallings, J.: Brick’s quasi-simple filtrations for groups and 3-manifolds, A conference proceedings paper in the Volume Geometric Group Theory 1, London Math. Soc., pp. 188–203 (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Poénaru, V. Equivariant, locally finite inverse representations with uniformly bounded zipping length, for arbitrary finitely presented groups. Geom Dedicata 167, 91–121 (2013). https://doi.org/10.1007/s10711-012-9805-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10711-012-9805-2
Keywords
- Finitely presented groups
- QSF (quasi-simply filtered)
- Geometric simple connectivity
- Zipping
- (Inverse) representations of groups