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2013 | 11 | 11 | 1932-1948
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Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

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We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied.
Twórcy
Bibliografia
  • [1] Banakh T., Valov V., General position properties in fiberwise geometric topology, preprint available at http://arxiv.org/abs/1001.2494
  • [2] Borel A., Seminar on Transformation Groups, Ann. of Math. Stud., 46, Princeton University Press, Princeton, 1960
  • [3] Cannon J.W., Daverman R.J., A totally wild flow, Indiana Univ. Math. J., 1981, 30(3), 371–387 http://dx.doi.org/10.1512/iumj.1981.30.30029
  • [4] Daverman R.J., Products of cell-like decomposition, Topology Appl., 1980, 11(2), 121–139 http://dx.doi.org/10.1016/0166-8641(80)90002-4
  • [5] Daverman R.J., Detecting the disjoint disks property, Pacific J. Math., 1981, 93(2), 277–298 http://dx.doi.org/10.2140/pjm.1981.93.277
  • [6] Daverman R.J., Decompositions of Manifolds, Pure Appl. Math., 124, Academic Press, Orlando, 1986
  • [7] Daverman R.J., Halverson D., Path concordances as detectors of codimension-one manifold factors, Exotic Homology Manifolds, Oberwolfach, June 29–July 5, 2003, Geom. Topol. Monogr., 9, Geometry & Topology Publications, Coventry, 2006, 7–15
  • [8] Daverman R.J., Halverson D.M., The cell-like approximation theorem in dimension 5, Fund. Math., 2007, 197, 81–121 http://dx.doi.org/10.4064/fm197-0-5
  • [9] Daverman R.J., Walsh J.J., A ghastly generalized n-manifold, Illinois J. Math., 1981, 25(4), 555–576
  • [10] Edwards R.D., The topology of manifolds and cell-like maps, Proceedings of the International Congress of Mathematicians, Helsinki, August 15-23, 1978, Academia Scientiarum Fennica, Helsinki, 1980, 111–127
  • [11] Halverson D.M., Detecting codimension one manifold factors with the disjoint homotopies property, Topology Appl., 2002, 117(3), 231–258 http://dx.doi.org/10.1016/S0166-8641(01)00022-0
  • [12] Halverson D.M., 2-ghastly spaces with the disjoint homotopies property: the method of fractured maps, Topology Appl., 2004, 138(1–3), 277–286 http://dx.doi.org/10.1016/j.topol.2003.08.016
  • [13] Halverson D.M., Detecting codimension one manifold factors with 0-stitched disks, Topology Appl., 2007, 154(9), 1993–1998 http://dx.doi.org/10.1016/j.topol.2007.02.006
  • [14] Halverson D.M., Repovš D., Detecting codimension one manifold factors with topographical techniques, Topology Appl., 2009, 156(17), 2870–2880 http://dx.doi.org/10.1016/j.topol.2009.08.023
  • [15] Halverson D.M., Repovš D., A survey on the generalized R. L. Moore Problem, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia, 2011, 58, 175–191
  • [16] Halverson D.M., Repovš D., Decompositions of ℝ, n ≥ 4, into convex sets generate codimension 1 manifold factors, Mediterr. J. Math., 2013, 10(2), 1101–1106 http://dx.doi.org/10.1007/s00009-012-0197-1
  • [17] Mitchell W.J.R., Repovš D., Topology of cell-like mappings, Rend. Sem. Fac. Sci. Univ. Cagliari, 1988, 58(suppl.), 265–300
  • [18] Moore R.L., Concerning upper semi-continuous collections of continua which do not separate a given continuum, Proc. Natl. Acad. Sci. USA, 1924, 10(8), 356–360 http://dx.doi.org/10.1073/pnas.10.8.356
  • [19] Moore R.L., Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc., 1925, 27(4), 416–428 http://dx.doi.org/10.1090/S0002-9947-1925-1501320-8
  • [20] Rourke C.P., Sanderson B.J., Introduction to Piecewise-Linear Topology, Ergeb. Math. Grenzgeb., 69, Springer, New York-Heidelberg, 1972 http://dx.doi.org/10.1007/978-3-642-81735-9
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