Algebraic & Geometric Topology Volume 21, issue 7 (2021)

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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

DOI: 10.2140/agt.2021.21.3221

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