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Intersection homology duality and pairings: singular, PL and sheaf-theoretic

Greg Friedman and James E McClure

Algebraic & Geometric Topology 21 (2021) 3221–3301
Bibliography
1 M Banagl, Topological invariants of stratified spaces, Springer (2007) MR2286904
2 A Borel, editor, Intersection cohomology, 50, Birkhäuser (1984) MR788171
3 J P Brasselet, G Hector, M Saralegi, Théorème de de Rham pour les variétés stratifiées, Ann. Global Anal. Geom. 9 (1991) 211 MR1143404
4 G E Bredon, Sheaf theory, 170, Springer (1997) MR1481706
5 J L Brylinski, Equivariant intersection cohomology, from: "Kazhdan–Lusztig theory and related topics" (editor V Deodhar), Contemp. Math. 139, Amer. Math. Soc. (1992) 5 MR1197827
6 H Cartan, S Eilenberg, Homological algebra, 19, Princeton Univ. Press (1956) MR0077480
7 D Chataur, M Saralegi-Aranguren, D Tanré, Blown-up intersection cohomology, from: "An alpine bouquet of algebraic topology" (editors C Ausoni, K Hess, B Johnson, I Moerdijk, J Scherer), Contemp. Math. 708, Amer. Math. Soc. (2018) 45 MR3807751
8 D Chataur, M Saralegi-Aranguren, D Tanré, Intersection cohomology, simplicial blow-up and rational homotopy, 1214, Amer. Math. Soc. (2018) MR3796432
9 D Chataur, M Saralegi-Aranguren, D Tanré, Intersection homology: general perversities and topological invariance, Illinois J. Math. 63 (2019) 127 MR3959870
10 D Chataur, M Saralegi-Aranguren, D Tanré, Blown-up intersection cochains and Deligne’s sheaves, Geom. Dedicata 204 (2020) 315 MR4056706
11 J Dieudonné, A history of algebraic and differential topology, 1900–1960, Birkhäuser (1989) MR995842
12 A Dimca, Sheaves in topology, Springer (2004) MR2050072
13 A Dold, Lectures on algebraic topology, 200, Springer (1972) MR0415602
14 G Friedman, Singular chain intersection homology for traditional and super-perversities, Trans. Amer. Math. Soc. 359 (2007) 1977 MR2276609
15 G Friedman, Intersection homology Künneth theorems, Math. Ann. 343 (2009) 371 MR2461258
16 G Friedman, On the chain-level intersection pairing for PL pseudomanifolds, Homology Homotopy Appl. 11 (2009) 261 MR2529162
17 G Friedman, Intersection homology with general perversities, Geom. Dedicata 148 (2010) 103 MR2721621
18 G Friedman, An introduction to intersection homology with general perversity functions, from: "Topology of stratified spaces" (editors G Friedman, E Hunsicker, A Libgober, L Maxim), Math. Sci. Res. Inst. Publ. 58, Cambridge Univ. Press (2011) 177 MR2796412
19 G Friedman, The chain-level intersection product for PL pseudomanifolds revisited, J. Singul. 17 (2018) 330 MR3857199
20 G Friedman, Singular intersection homology, 33, Cambridge Univ. Press (2020)
21 G Friedman, J E McClure, Cup and cap products in intersection (co)homology, Adv. Math. 240 (2013) 383 MR3046315
22 S I Gelfand, Y I Manin, Methods of homological algebra, Springer (2003) MR1950475
23 M Goresky, R MacPherson, Intersection homology theory, Topology 19 (1980) 135 MR572580
24 M Goresky, R MacPherson, Intersection homology, II, Invent. Math. 72 (1983) 77 MR696691
25 M Goresky, P Siegel, Linking pairings on singular spaces, Comment. Math. Helv. 58 (1983) 96 MR699009
26 N Habegger, From PL to sheaf theory (rock to Bach), from: "Intersection cohomology" (editor A Borel), Progr. Math. 50, Birkhäuser (1984) 23 MR788173
27 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
28 P J Hilton, U Stammbach, A course in homological algebra, 4, Springer (1971) MR0346025
29 B Iversen, Cohomology of sheaves, Springer (1986) MR842190
30 M Kashiwara, P Schapira, Sheaves on manifolds, 292, Springer (1990) MR1074006
31 H C King, Topological invariance of intersection homology without sheaves, Topology Appl. 20 (1985) 149 MR800845
32 F Kirwan, J Woolf, An introduction to intersection homology theory, Chapman & Hall (2006) MR2207421
33 T Y Lam, Lectures on modules and rings, 189, Springer (1999) MR1653294
34 J E McClure, On the chain-level intersection pairing for PL manifolds, Geom. Topol. 10 (2006) 1391 MR2255502
35 J R Munkres, Elements of algebraic topology, CRC (1984) MR755006
36 G Padilla, On normal stratified pseudomanifolds, Extracta Math. 18 (2003) 223 MR2002448
37 M Saralegi, Homological properties of stratified spaces, Illinois J. Math. 38 (1994) 47 MR1245833
38 M Saralegi-Aranguren, de Rham intersection cohomology for general perversities, Illinois J. Math. 49 (2005) 737 MR2210257
39 M Saralegi-Aranguren, D Tanré, Poincaré duality, cap product and Borel–Moore intersection homology, Q. J. Math. 71 (2020) 943 MR4142716
40 E G Sklyarenko, On the nature of homological multiplications and duality, Uspekhi Mat. Nauk 49 (1994) 141 MR1307132
41 R G Swan, The theory of sheaves, Univ. Chicago Press (1964)
42 R O Wells Jr., Differential analysis on complex manifolds, Prentice-Hall (1973) MR0515872