Geometry & Topology Volume 11, issue 3 (2007)

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Hodge and signature theorems for a family of manifolds with fibre bundle boundary

Eugénie Hunsicker

Geometry & Topology 11 (2007) 1581–1622

DOI: 10.2140/gt.2007.11.1581

Bibliography

1	M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43 MR0397797
2	M F Atiyah, I M Singer, The index of elliptic operators. III, Ann. of Math. $(2)$ 87 (1968) 546 MR0236952
3	J M Bismut, J Cheeger, $\eta$-invariants and their adiabatic limits, J. Amer. Math. Soc. 2 (1989) 33 MR966608
4	J Brüning, M Lesch, Hilbert complexes, J. Funct. Anal. 108 (1992) 88 MR1174159
5	J Cheeger, On the spectral geometry of spaces with cone-like singularities, Proc. Nat. Acad. Sci. U.S.A. 76 (1979) 2103 MR530173
6	J Cheeger, On the Hodge theory of Riemannian pseudomanifolds, from: "Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979)", Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc. (1980) 91 MR573430
7	J Cheeger, X Dai, $L^2$-cohomology of a non-isolated conical singularity and nonmultiplicativity of the signature, preprint
8	S S Chern, F Hirzebruch, J P Serre, On the index of a fibered manifold, Proc. Amer. Math. Soc. 8 (1957) 587 MR0087943
9	P E Conner, The Neumann's problem for differential forms on Riemannian manifolds, Mem. Amer. Math. Soc. 1956 (1956) 56 MR0078467
10	X Dai, Adiabatic limits, nonmultiplicativity of signature, and Leray spectral sequence, J. Amer. Math. Soc. 4 (1991) 265 MR1088332
11	M Goresky, R MacPherson, Intersection homology theory, Topology 19 (1980) 135 MR572580
12	M Goresky, R MacPherson, Intersection homology. II, Invent. Math. 72 (1983) 77 MR696691
13	M Goresky, R MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 14, Springer (1988) MR932724
14	N Habegger, L Saper, Intersection cohomology of cs-spaces and Zeeman's filtration, Invent. Math. 105 (1991) 247 MR1115543
15	T Hausel, E Hunsicker, R Mazzeo, Hodge cohomology of gravitational instantons, Duke Math. J. 122 (2004) 485 MR2057017
16	E Hunsicker, R Mazzeo, Harmonic forms on manifolds with edges, Int. Math. Res. Not. (2005) 3229 MR2186793
17	H C King, Topological invariance of intersection homology without sheaves, Topology Appl. 20 (1985) 149 MR800845
18	R R Mazzeo, R B Melrose, The adiabatic limit, Hodge cohomology and Leray's spectral sequence for a fibration, J. Differential Geom. 31 (1990) 185 MR1030670
19	C McCrory, Zeeman's filtration of homology, Trans. Amer. Math. Soc. 250 (1979) 147 MR530047
20	W Müller, $L^2$-index theory, eta invariants and values of $L$-functions, from: "Geometric and topological invariants of elliptic operators (Brunswick, ME, 1988)", Contemp. Math. 105, Amer. Math. Soc. (1990) 145 MR1047280
21	M Nagase, $L^{2}$-cohomology and intersection homology of stratified spaces, Duke Math. J. 50 (1983) 329 MR700144
22	E C Zeeman, Dihomology. III. A generalization of the Poincaré duality for manifolds, Proc. London Math. Soc. $(3)$ 13 (1963) 155 MR0153011
23	S Zucker, $L_{2}$ cohomology of warped products and arithmetic groups, Invent. Math. 70 (1982/83) 169 MR684171