Algebraic & Geometric Topology Volume 13, issue 4 (2013)

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$\mathit{UV}^k$–mappings on homology manifolds

John Bryant, Steve Ferry and Washington Mio

Algebraic & Geometric Topology 13 (2013) 2141–2170

DOI: 10.2140/agt.2013.13.2141

Bibliography

1	R D Anderson, Open mappings of compact continua, Proc. Nat. Acad. Sci. U. S. A. 42 (1956) 347 MR0078682
2	M Bestvina, Characterizing $k$–dimensional universal Menger compacta, Mem. Amer. Math. Soc. 71 (1988) MR920964
3	J L Bryant, On embeddings of compacta in Euclidean space, Proc. Amer. Math. Soc. 23 (1969) 46 MR0244973
4	J L Bryant, General position theorems for generalized manifolds, Proc. Amer. Math. Soc. 98 (1986) 667 MR861772
5	J Bryant, S Ferry, W Mio, S Weinberger, Topology of homology manifolds, Ann. of Math. 143 (1996) 435 MR1394965
6	J Bryant, S Ferry, W Mio, S Weinberger, Desingularizing homology manifolds, Geom. Topol. 11 (2007) 1289 MR2326946
7	J L Bryant, W Mio, Embeddings of homology manifolds in codimension $\ge3$, Topology 38 (1999) 811 MR1679800
8	T A Chapman, Lectures on Hilbert cube manifolds, Regional Conf. Series Math. 28, Amer. Math. Soc. (1976) MR0423357
9	T A Chapman, S Ferry, Approximating homotopy equivalences by homeomorphisms, Amer. J. Math. 101 (1979) 583 MR533192
10	A V Chernavskiĭ, Generalization of L\thinspaceV Keldysh's construction, of a monotone mapping of a cube, to a cube of higher dimension, Uspekhi Mat. Nauk 40 (1985) 209 MR807759
11	S Ferry, Homotoping $\varepsilon $–maps to homeomorphisms, Amer. J. Math. 101 (1979) 567 MR533191
12	S C Ferry, Constructing $UV^k$–maps between spheres, Proc. Amer. Math. Soc. 120 (1994) 329 MR1166355
13	S C Ferry, Epsilon-delta surgery over $\mathbb{Z}$, Geom. Dedicata 148 (2010) 71 MR2721620
14	R L Frum-Ketkov, Homological properties of original point images in the case of manifold mappings increasing the dimension, Dokl. Akad. Nauk SSSR 122 (1958) 349 MR0132544
15	W Hurewicz, H Wallman, Dimension Theory, Princeton Mathematical Series 4, Princeton Univ. Press (1941) MR0006493
16	L Keldyš, Monotone mapping of a cube onto a cube of higher dimension, Mat. Sb. N.S. 41(83) (1957) 129 MR0090805
17	P Krupski, Recent results on homogeneous curves and ANRs, Topology Proc. 16 (1991) 109 MR1206457
18	R C Lacher, Cell-like mappings. I, Pacific J. Math. 30 (1969) 717 MR0251714
19	R C Lacher, Cell-like mappings. II, Pacific J. Math. 35 (1970) 649 MR0281217
20	R C Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc. 83 (1977) 495 MR0645403
21	S Mardešić, Strong shape and homology, Springer (2000) MR1740831
22	R T Miller, Mapping cylinder neighborhoods of some ANR's, Ann. of Math. 103 (1976) 417 MR0402757
23	W J R Mitchell, Defining the boundary of a homology manifold, Proc. Amer. Math. Soc. 110 (1990) 509 MR1019276
24	E K Pedersen, F Quinn, A Ranicki, Controlled surgery with trivial local fundamental groups, from: "High-dimensional manifold topology" (editors F T Farrell, W Lück), World Sci. Publ. (2003) 421 MR2048731
25	F Quinn, Ends of maps. I, Ann. of Math. 110 (1979) 275 MR549490
26	F Quinn, Resolutions of homology manifolds, and the topological characterization of manifolds, Invent. Math. 72 (1983) 267 MR700771
27	C P Rourke, B J Sanderson, Introduction to piecewise-linear topology, Springer (1982) MR665919
28	M A Štan’ko, Imbedding of compacta in euclidean space, Mat. Sb. 83 (125) (1970) 234 MR0271923
29	J J Walsh, General position properties of generalized manifolds: a primer, Proc. Idaho State Topology Conf. (1985)
30	J J Walsh, A general method of constructing $UV^k$-mappings on manifolds with applications to spheres, Preprint (1974)
31	D C Wilson, Monotone mappings of manifolds onto cells, from: "Proc. First Conf. on Monotone Mappings and Open Mappings" (editor L F McCauley), State Univ. of New York at Binghamton (1971) 37 MR0279780
32	D C Wilson, On constructing monotone and $UV^{1}$ mappings of arbitrary degree, Duke Math. J. 41 (1974) 103 MR0339250