Volume 23, issue 5 (2019)

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

Volume 29, 1 issue

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

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 Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Hodge theory for intersection space cohomology

Markus Banagl and Eugénie Hunsicker

Geometry & Topology 23 (2019) 2165–2225
Bibliography
1 M Banagl, Topological invariants of stratified spaces, Springer (2007) MR2286904
2 M Banagl, Intersection spaces, spatial homology truncation, and string theory, 1997, Springer (2010) MR2662593
3 M Banagl, Isometric group actions and the cohomology of flat fiber bundles, Groups Geom. Dyn. 7 (2013) 293 MR3054571
4 M Banagl, Foliated stratified spaces and a de Rham complex describing intersection space cohomology, J. Differential Geom. 104 (2016) 1 MR3544285
5 M Banagl, N Budur, L Maxim, Intersection spaces, perverse sheaves and type IIB string theory, Adv. Theor. Math. Phys. 18 (2014) 363 MR3273317
6 M Banagl, S E Cappell, J L Shaneson, Computing twisted signatures and L–classes of stratified spaces, Math. Ann. 326 (2003) 589 MR1992279
7 M Banagl, B Chriestenson, Intersection spaces, equivariant Moore approximation and the signature, J. Singul. 16 (2017) 141 MR3687584
8 M Banagl, L Maxim, Deformation of singularities and the homology of intersection spaces, J. Topol. Anal. 4 (2012) 413 MR3021771
9 M Banagl, L Maxim, Intersection spaces and hypersurface singularities, J. Singul. 5 (2012) 48 MR2928933
10 R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) MR658304
11 J P Brasselet, G Hector, M Saralegi, Théorème de de Rham pour les variétés stratifiées, Ann. Global Anal. Geom. 9 (1991) 211 MR1143404
12 D Chataur, M Saralegi-Aranguren, D Tanré, Intersection cohomology, simplicial blow-up and rational homotopy, 1214, Amer. Math. Soc. (2018) MR3796432
13 J Cheeger, On the spectral geometry of spaces with cone-like singularities, Proc. Nat. Acad. Sci. U.S.A. 76 (1979) 2103 MR530173
14 J Cheeger, On the Hodge theory of Riemannian pseudomanifolds, from: "Geometry of the Laplace operator" (editors R Osserman, A Weinstein), Proc. Sympos. Pure Math. 36, Amer. Math. Soc. (1980) 91 MR573430
15 J Cheeger, Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18 (1983) 575 MR730920
16 T Essig, About a de Rham complex describing intersection space cohomology in a non-isolated singularity case, Diplomarbeit, Ruprecht-Karls-Universität Heidelberg (2012)
17 G Friedman, Singular intersection homology, book project (2019)
18 G Friedman, E Hunsicker, Additivity and non-additivity for perverse signatures, J. Reine Angew. Math. 676 (2013) 51 MR3028755
19 G Friedman, J E McClure, Cup and cap products in intersection (co)homology, Adv. Math. 240 (2013) 383 MR3046315
20 M Goresky, R MacPherson, Intersection homology theory, Topology 19 (1980) 135 MR572580
21 M Goresky, R MacPherson, Intersection homology, II, Invent. Math. 72 (1983) 77 MR696691
22 D Grieser, E Hunsicker, Pseudodifferential operator calculus for generalized –rank 1 locally symmetric spaces, II, in preparation
23 T Hausel, E Hunsicker, R Mazzeo, Hodge cohomology of gravitational instantons, Duke Math. J. 122 (2004) 485 MR2057017
24 E Hunsicker, Hodge and signature theorems for a family of manifolds with fibre bundle boundary, Geom. Topol. 11 (2007) 1581 MR2326952
25 E Hunsicker, Extended Hodge theory for fibred cusp manifolds, J. Topol. Anal. 10 (2018) 531 MR3850103
26 H C King, Topological invariance of intersection homology without sheaves, Topology Appl. 20 (1985) 149 MR800845
27 M Klimczak, Poincaré duality for spaces with isolated singularities, Manuscripta Math. 153 (2017) 231 MR3635981
28 E Kreyszig, Introductory functional analysis with applications, Wiley (1989) MR992618
29 J M Lee, Introduction to smooth manifolds, 218, Springer (2003) MR1930091
30 R B Melrose, The Atiyah–Patodi–Singer index theorem, 4, A K Peters (1993) MR1348401
31 M Saralegi-Aranguren, De Rham intersection cohomology for general perversities, Illinois J. Math. 49 (2005) 737 MR2210257
32 S Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds, Tôhoku Math. J. 10 (1958) 338 MR0112152
33 P H Siegel, Witt spaces : a geometric cycle theory for KO–homology at odd primes, Amer. J. Math. 105 (1983) 1067 MR714770
34 E H Spanier, Algebraic topology, McGraw-Hill (1966) MR0210112
35 M Spiegel, K–theory of intersection spaces, PhD thesis, Ruprecht-Karls-Universität Heidelberg (2013)