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Obstructions to stably fibering manifolds

Wolfgang Steimle

Geometry & Topology 16 (2012) 1691–1724
Bibliography
1 D R Anderson, The Whitehead torsion of a fiber-homotopy equivalence, Michigan Math. J. 21 (1974) 171 MR0343283
2 M Bökstedt, F Waldhausen, The map $BSG\to A(*)\to QS^ 0$, from: "Algebraic topology and algebraic $K$–theory (Princeton, NJ, 1983)" (editor W Browder), Ann. of Math. Stud. 113, Princeton Univ. Press (1987) 418 MR921487
3 W Browder, J Levine, Fibering manifolds over a circle, Comment. Math. Helv. 40 (1966) 153 MR0195104
4 G W Brumfiel, Homotopy equivalences of almost smooth manifolds, from: "Algebraic topology (Proc. Sympos. Pure Math., Vol. XXII, Univ. Wisconsin, Madison, WI., 1970)" (editor A Liulevicius), Amer. Math. Soc. (1971) 73 MR0319217
5 D Burghelea, Converting compact ANR fibrations into locally trivial bundles with compact manifolds as fibres, Compositio Math. 49 (1983) 95 MR699861
6 A J Casson, Fibrations over spheres, Topology 6 (1967) 489 MR0217809
7 T A Chapman, Lectures on Hilbert cube manifolds, Regional Conference Series in Math. 28, Amer. Math. Soc. (1976) MR0423357
8 T A Chapman, S Ferry, Fibering Hilbert cube manifolds over ANRs, Compositio Math. 36 (1978) 7 MR515035
9 W Dwyer, M Weiss, B Williams, A parametrized index theorem for the algebraic $K$–theory Euler class, Acta Math. 190 (2003) 1 MR1982793
10 F T Farrell, The obstruction to fibering a manifold over a circle, Indiana Univ. Math. J. 21 (1971/1972) 315 MR0290397
11 F T Farrell, W Lück, W Steimle, Obstructions to fibering a manifold, Geom. Dedicata 148 (2010) 35 MR2721619
12 M H Freedman, F Quinn, Topology of $4$–manifolds, Princeton Math. Series 39, Princeton Univ. Press (1990) MR1201584
13 A E Hatcher, Concordance spaces, higher simple-homotopy theory, and applications, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, CA, 1976), Part 1" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 3 MR520490
14 F Hirzebruch, Topological methods in algebraic geometry, Classics in Math., Springer (1995) MR1335917
15 S L Hoehn, The moduli space of compact fiber bundle structures on a fibration, PhD thesis, University of Notre Dame (2009)
16 K Igusa, What happens to Hatcher and Wagoner's formulas for $\pi_{0}C(M)$ when the first Postnikov invariant of $M$ is nontrivial?, from: "Algebraic $K$–theory, number theory, geometry and analysis (Bielefeld, 1982)" (editor A Bak), Lecture Notes in Math. 1046, Springer (1984) 104 MR750679
17 K Igusa, The stability theorem for smooth pseudoisotopies, $K$–Theory 2 (1988) MR972368
18 R C Kirby, L C Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Annals of Math. Studies 88, Princeton Univ. Press (1977) MR0645390
19 J R Klein, B Williams, The refined transfer, bundle structures, and algebraic $K$–theory, J. Topol. 2 (2009) 321 MR2529299
20 R C Lacher, Cell-like mappings, I, Pacific J. Math. 30 (1969) 717 MR0251714
21 W Lück, The transfer maps induced in the algebraic $K_0$– and $K_1$–groups by a fibration II, J. Pure Appl. Algebra 45 (1987) 143 MR889589
22 I Madsen, R J Milgram, The classifying spaces for surgery and cobordism of manifolds, Annals of Math. Studies 92, Princeton Univ. Press (1979) MR548575
23 J Milnor, On spaces having the homotopy type of a $\mathrm{CW}$–complex, Trans. Amer. Math. Soc. 90 (1959) 272 MR0100267
24 F Quinn, A geometric formulation of surgery, from: "Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, GA, 1969)" (editors J C Cantrell, C H Edwards), Markham (1970) 500 MR0282375
25 R Reis, M Weiss, Smooth maps to the plane and Pontryagin classes, part II: Homotopy theory arXiv:1102.0233
26 L C Siebenmann, A total Whitehead torsion obstruction to fibering over the circle, Comment. Math. Helv. 45 (1970) 1 MR0287564
27 W Steimle, Whitehead-Torsion und Faserungen arXiv:0706.3973
28 W Steimle, Obstructions to stably fibering manifolds, PhD thesis, Universität Münster (2010)
29 W Steimle, Higher Whitehead torsion and the geometric assembly map, to appear in J. Topol. arXiv:1105.2116
30 F Waldhausen, Algebraic $K$–theory of topological spaces. I, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, CA, 1976), Part 1" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 35 MR520492
31 F Waldhausen, Algebraic $K$–theory of spaces, a manifold approach, from: "Current trends in algebraic topology, Part 1 (London, ON, 1981)" (editors R M Kane, S O Kochman, P S Selick, V P Snaith), CMS Conf. Proc. 2, Amer. Math. Soc. (1982) 141 MR686115
32 C T C Wall, Finiteness conditions for $\mathrm{CW}$–complexes, Ann. of Math. 81 (1965) 56 MR0171284
33 C T C Wall, Classification problems in differential topology—IV: Thickenings, Topology 5 (1966) 73 MR0192509
34 M Weiss, B Williams, Automorphisms of manifolds, from: "Surveys on surgery theory, Vol. 2" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 149, Princeton Univ. Press (2001) 165 MR1818774