Volume 16, issue 3 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 8, 3307–3833
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
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