Peripheral acyclicity and homology manifolds

Annali di Matematica Pura ed Applicata

Volumn 172, Issue 1, 1997, Pages 5-24

  Cavicchioli, Alberto ^a   Repovš, Dušan ^b,c  

^a UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

^b UNIVERSITY OF TRIESTE   (Italy)

^c UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845190944     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/BF01782604     Document Type: Article

References (43)

1. J. J. ANDREWS - M. L. CURTIS, n-space modulo an arc, Ann. Math., 75 (1962), pp. 1-7.
2. S. ARMENTROUT, UV properties of compact sets, Trans. Amer. Math. Soc., 143 (1969), pp. 487-498.
3. S. ARMENTROUT, Homotopy properties of decomposition spaces, Trans. Amer. Math. Soc., 143 (1969), pp. 499-507.
4. 4, Ann. Math., 70 (1959), pp. 399-412.
5. W. A. BLANKINSHIP, Generalization of a construction of Antoine, Ann. Math., 53 (1951), pp. 276-297.
6. J. BRYANT- S. FERRY- W. MIO- S. WEINBERGER, Topology of homology manifolds, Bull. Amer. Math. Soc., 28 (1993), pp. 324-328.
7. M. BROWN, A proof of the generalized Schoenflies Theorem, Bull. Amer. Math. Soc., 66 (1960), pp. 74-76.
8. S. BUONCRISTIANO - C. P. ROURKE - B. J. SANDERSON, A Geometric Approach to Homology Theory, London Math. Soc., Lect. Notes Ser. 18, Cambridge Univ. Press, Cambridge-London-New York (1975).
9. S. BUONCRISTIANO, Coomologia di Goresky-Mac Pherson nella categoria PL, Suppl. Rend. Circ. Mat. Palermo, 4 (1984), pp. 13-19.
10. S. BUONCRISTIANO, Homology manifolds, homology bundles and characteristic numbers, Note di Matematica, 9 (1989), pp. 73-83.
11. 5/G, Rocky Mountain J. Math., 8 (1978), pp. 527-532.
12. J. W. CANNON, The recognition problem: What is a topological manifold?, Bull. Amer. Math. Soc., 84 (1978), pp. 832-866.
13. A. CAVICCHIOLI, Pseudo-dissezioni e triangolazioni contratte di spazi con singolarità isolate, Atti Sem. Mat. Fis. Univ. Modena, 27 (1978), pp. 132-150.
14. A. CAVICCHIOLI, Imbeddings of polyhedra in 3-manifolds, Ann. Mat. Pura Appl., 162 (1992), pp. 157-177.
15. A. CAVICCHIOLI - F. HEGENBARTH - D. REPOVŠ, The Topology of Homology Manifolds and Cell-like Maps, to appear.
16. R. J. DAVERMAN, Decompositions of Manifolds, Academic Press, London-New York-Tokyo (1986).
17. R. J. DAVERMAN, Detecting the disjoint disks property, Pacific J. Math., 93 (1981), pp. 277-298.
18. R. J. DAVERMAN - D. REPOVŠ, A new 3-dimensional shrinking theorem, Trans. Amer. Math. Soc., 315 (1989), pp. 219-230.
19. R. J. DAVERMAN - D. REPOVŠ, General position properties that characterize 3-manifolds, Canad. J. Math., 44 (1992), pp. 234-251.
20. R. D. EDWARDS, Approximating certain cell-like maps by homeomorphisms, Notices Amer. Math. Soc., 24 (1977), pp. 649.
21. R. D. EDWARDS, The topology of manifolds and cell-like maps, in Proc. Internat. Congr. Math. Helsinki (O. LEHTO Ed.), Acad. Sci. Fenn., Helsinki (1980), pp. 111-127.
22. R. H. FOX - E. ARTIN, Some wild cells and spheres in three-dimensional space, Ann. of Math., 49 (1948), pp. 979-990.
23. M. H. FREEDMAN, The topology of four-dimensional manifolds, J. Diff. Geom., 17 (1982), pp. 357-453.
24. M. H. FREEDMAN - F. LUO, Selected Applications of Geometry to Low-dimensional Topology, Amer. Math. Soc. Univ. Lect. Ser. 1, Providence, Rhode Island (1987).
25. M. H. FREEDMAN - F. QUINN, Topology of 4-Manifolds, Princeton Univ. Press, Princeton, New Jersey (1990).
26. J. HEMPEL, 3-Manifolds, Princeton Univ. Press, Princeton, New Jersey (1976).
27. J. F. P. HUDSON, Piecewise Linear Topology, W. A. Benjamin Inc., New York-Amsterdam (1969).
28. R. C. KIRBY, The Topology of 4-Manifolds, Lect. Notes in Math. 1374, Springer-Verlag, Berlin-Heidelberg-New York (1989).
29. R. C. LACHER, A cellularity criterion based on codimension, Glasnik Mat., 11 (1976), pp. 135-140.
30. R. C. LACHER, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc., 83 (1977), pp. 495-552.
31. D. R. MCMILLAN JR., A criterion for cellularity in a manifold, Ann. of Math., 79 (1964), pp. 327-337;
32. Trans. Amer. Math. Soc., 126 (1967) pp. 217-224.
33. D. R. MCMILLAN JR., Compact, acyclic subsets of three-manifolds, Michigan Math. J., 36 (1969), pp. 129-136.
34. D. R. MCMILLAN JR., Acyclicity in three-manifolds, Bull. Amer. Math. Soc., 76 (1970), pp. 942-964.
35. W. J. R. MITCHELL - D. REPOVŠ, The topology of cell-like mappings, in Proc. Conf. on Diff. Geometry and Topology, Cala Gonone (Sardegna), 26/30 Sept. 1988, Rend. Sem. Facoltà Scienze Univ. Cagliari, 58 (1988), pp. 265-300.
36. F. QUINN, Resolutions of homology manifolds and the topological characterization of manifolds, Invent. Math., 72, (1983), pp. 267-284; Corrigendum, Invent. Math., 85 (1986), pp. 653.
37. F. QUINN, An obstruction to the resolution of homology manifolds, Michigan Math. J., 301 (1987), pp. 285-292.
38. D. REPOVŠ, Peripheral acyclicity in 3-manifolds, J. Austral. Math. Soc., Ser. A, 42 (1987), pp. 312-321.
39. D. REPOVŠ, A criterion for cellularity in a topological 4-manifold, Proc. Amer. Math. Soc., 100 (1987), pp. 564-566.
40. D. REPOVŠ, Regular neighbourhoods of homotopically PL embedded compacta in 3-manifolds, Suppl. Rend. Circ. Mat. Palermo, 18 (1988), pp. 415-422.
41. D. REPOVŠ, Detection of higher dimensional topological manifolds among topological spaces, Seminari di Geometria, Dip. Mat. Univ. Bologna (1992), pp. 113-143.
42. L. C. SIEBENMANN, On detecting Euclidean space homotopically among topological manifolds, Invent. Math., 6 (1968), pp. 245-261.
43. E. C. ZEEMAN, On the dunce hat, Topology, 2 (1963) pp. 341-358.