Geometry & Topology Volume 11, issue 1 (2007)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Other MSP Journals

The signature of a fibre bundle is multiplicative mod 4

Ian Hambleton, Andrew Korzeniewski and Andrew Ranicki

Geometry & Topology 11 (2007) 251–314

DOI: 10.2140/gt.2007.11.251

Bibliography

1	D R Anderson, The Whitehead torsion of the total space of a fiber bundle, Topology 11 (1972) 179 MR0295348
2	M F Atiyah, The signature of fibre-bundles, from: "Global Analysis (Papers in Honor of K. Kodaira)", Univ. Tokyo Press (1969) 73 MR0254864
3	A J Casson, Generalisations and applications of block bundles, from: "The Hauptvermutung book", K–Monogr. Math. 1, Kluwer Acad. Publ. (1996) 33 MR1434102
4	S S Chern, F Hirzebruch, J P Serre, On the index of a fibered manifold, Proc. Amer. Math. Soc. 8 (1957) 587 MR0087943
5	H Endo, A construction of surface bundles over surfaces with non-zero signature, Osaka J. Math. 35 (1998) 915 MR1659565
6	I Hambleton, A Ranicki, L Taylor, Round $L$–theory, J. Pure Appl. Algebra 47 (1987) 131 MR906966
7	F Hirzebruch, The signature of ramified coverings, from: "Global Analysis (Papers in Honor of K. Kodaira)", Univ. Tokyo Press (1969) 253 MR0258060
8	F Hirzebruch, W D Neumann, S S Koh, Differentiable manifolds and quadratic forms, Lecture Notes in Pure and Applied Mathematics 4, Marcel Dekker (1971) MR0341499
9	S Klaus, P Teichner, Private communication (2003)
10	K Kodaira, A certain type of irregular algebraic surfaces, J. Analyse Math. 19 (1967) 207 MR0216521
11	A J Korzeniewski, Absolute Whitehead torsion, Geom. Topol. 11 (2007) 215
12	W Lück, The transfer maps induced in the algebraic $K_0$– and $K_1$–groups by a fibration. I, Math. Scand. 59 (1986) 93 MR873491
13	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
14	W Lück, A Ranicki, Surgery obstructions of fibre bundles, J. Pure Appl. Algebra 81 (1992) 139 MR1176019
15	S Maumary, Contributions à la théorie du type simple d'homotopie, Comment. Math. Helv. 44 (1969) 410 MR0266210
16	W Meyer, Die Signatur von Flächenbündeln, Math. Ann. 201 (1973) 239 MR0331382
17	J Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358 MR0196736
18	H J Munkholm, Whitehead torsion for PL fiber homotopy equivalences, from: "Algebraic topology, Waterloo, 1978 (Proc. Conf., Univ. Waterloo, Waterloo, Ont., 1978)", Lecture Notes in Math. 741, Springer (1979) 90 MR557164
19	W D Neumann, Multiplicativity of signature, J. Pure Appl. Algebra 13 (1978) 19 MR508726
20	E K Pedersen, Geometrically defined transfers, comparisons, Math. Z. 180 (1982) 535 MR667007
21	H Putz, Triangulation of fibre bundles, Canad. J. Math. 19 (1967) 499 MR0212810
22	A Ranicki, The algebraic theory of surgery. I. Foundations, Proc. London Math. Soc. $(3)$ 40 (1980) 87 MR560997
23	A Ranicki, The algebraic theory of surgery. II. Applications to topology, Proc. London Math. Soc. $(3)$ 40 (1980) 193 MR566491
24	A Ranicki, The algebraic theory of torsion. I. Foundations, from: "Algebraic and geometric topology (New Brunswick, N.J., 1983)", Lecture Notes in Math., Springer (1985) 199 MR802792
25	A Ranicki, The algebraic theory of torsion. II. Products, K–Theory 1 (1987) 115 MR899919
26	A Ranicki, Additive $L$–theory, K–Theory 3 (1989) 163 MR1029957
27	H Seifert, W Threlfall, Seifert and Threlfall: a textbook of topology, Pure and Applied Mathematics 89, Academic Press (1980) MR575168
28	C T C Wall, Surgery on compact manifolds, London Mathematical Society Monographs 1, Academic Press (1970) MR0431216
29	J H C Whitehead, Simple homotopy types, Amer. J. Math. 72 (1950) 1 MR0035437