Geometry & Topology Volume 13, issue 4 (2009)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Intersection homology and Poincaré duality on homotopically stratified spaces

Greg Friedman

Geometry & Topology 13 (2009) 2163–2204

DOI: 10.2140/gt.2009.13.2163

Bibliography

1	M Banagl, Extending intersection homology type invariants to non-Witt spaces, Mem. Amer. Math. Soc. 160 (2002) MR1937924
2	M Banagl, The $L$–class of non-Witt spaces, Ann. of Math. $(2)$ 163 (2006) 743 MR2215133
3	M Banagl, Topological invariants of stratified spaces, Springer Monogr. in Math., Springer (2007) MR2286904
4	M Banagl, S E Cappell, J L Shaneson, Computing twisted signatures and $L$–classes of stratified spaces, Math. Ann. 326 (2003) 589 MR1992279
5	A A Beĭlinson, J Bernstein, P Deligne, Faisceaux pervers, from: "Analysis and topology on singular spaces, I (Luminy, 1981)", Astérisque 100, Soc. Math. France (1982) 5 MR751966
6	A Beshears, $G$–isovariant structure sets and stratified structure sets, PhD thesis, Vanderbilt University (1997)
7	A Borel, e al, Intersection cohomology, Progress in Math. 50, Birkhäuser (1984) MR788171
8	G E Bredon, Sheaf theory, Graduate Texts in Math. 170, Springer (1997) MR1481706
9	J L Brylinski, Equivariant intersection cohomology, from: "Kazhdan–Lusztig theory and related topics (Chicago, IL, 1989)" (editor V Deodhar), Contemp. Math. 139, Amer. Math. Soc. (1992) 5 MR1197827
10	S E Cappell, J L Shaneson, Singular spaces, characteristic classes, and intersection homology, Ann. of Math. $(2)$ 134 (1991) 325 MR1127478
11	S E Cappell, J L Shaneson, Stratifiable maps and topological invariants, J. Amer. Math. Soc. 4 (1991) 521 MR1102578
12	S E Cappell, J L Shaneson, The mapping cone and cylinder of a stratified map, from: "Prospects in topology (Princeton, NJ, 1994)" (editor F Quinn), Ann. of Math. Stud. 138, Princeton Univ. Press (1995) 58 MR1368653
13	S E Cappell, J L Shaneson, S Weinberger, Classes topologiques caractéristiques pour les actions de groupes sur les espaces singuliers, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991) 293 MR1126399
14	S E Cappell, S Weinberger, Classification de certains espaces stratifiés, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991) 399 MR1126422
15	S J Curran, Intersection homology and free group actions on Witt spaces, Michigan Math. J. 39 (1992) 111 MR1137893
16	G Friedman, Stratified fibrations and the intersection homology of the regular neighborhoods of bottom strata, Topology Appl. 134 (2003) 69 MR2009092
17	G Friedman, Intersection homology of regular and cylindrical neighborhoods, Topology Appl. 149 (2005) 97 MR2130860
18	G Friedman, Superperverse intersection cohomology: stratification (in)dependence, Math. Z. 252 (2006) 49 MR2209151
19	G Friedman, Intersection homology of stratified fibrations and neighborhoods, Adv. Math. 215 (2007) 24 MR2354985
20	G Friedman, Singular chain intersection homology for traditional and super-perversities, Trans. Amer. Math. Soc. 359 (2007) 1977 MR2276609
21	M Goresky, R MacPherson, Intersection homology theory, Topology 19 (1980) 135 MR572580
22	M Goresky, R MacPherson, Intersection homology. II, Invent. Math. 72 (1983) 77 MR696691
23	M Goresky, P Siegel, Linking pairings on singular spaces, Comment. Math. Helv. 58 (1983) 96 MR699009
24	N Habegger, L Saper, Intersection cohomology of cs-spaces and Zeeman's filtration, Invent. Math. 105 (1991) 247 MR1115543
25	G Hector, M Saralegi, Intersection cohomology of $S^1$–actions, Trans. Amer. Math. Soc. 338 (1993) 263 MR1116314
26	B Hughes, Stratifications of mapping cylinders, Topology Appl. 94 (1999) 127 MR1695351
27	B Hughes, Stratified path spaces and fibrations, Proc. Roy. Soc. Edinburgh Sect. A 129 (1999) 351 MR1686706
28	B Hughes, The approximate tubular neighborhood theorem, Ann. of Math. $(2)$ 156 (2002) 867 MR1954237
29	B Hughes, A Ranicki, Ends of complexes, Cambridge Tracts in Math. 123, Cambridge Univ. Press (1996) MR1410261
30	B Hughes, L R Taylor, S Weinberger, B Williams, Neighborhoods in stratified spaces with two strata, Topology 39 (2000) 873 MR1763954
31	B Hughes, S Weinberger, Surgery and stratified spaces, from: "Surveys on surgery theory, Vol. 2" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 149, Princeton Univ. Press (2001) 319 MR1818777
32	W Hurewicz, H Wallman, Dimension theory, Princeton Math. Ser. 4, Princeton Univ. Press (1941) MR0006493
33	H C King, Topological invariance of intersection homology without sheaves, Topology Appl. 20 (1985) 149 MR800845
34	F Kirwan, An introduction to intersection homology theory, Pitman Research Notes in Math. Series 187, Longman Scientific & Technical (1988) MR981185
35	S L Kleiman, The development of intersection homology theory, Pure Appl. Math. Q. 3 (2007) 225 MR2330160
36	G Padilla, Intersection cohomology of stratified circle actions, Illinois J. Math. 49 (2005) 659 MR2164356
37	G Padilla, M Saralegi-Aranguren, Intersection cohomology of the circle actions, Topology Appl. 154 (2007) 2764 MR2344739
38	F Quinn, Intrinsic skeleta and intersection homology of weakly stratified sets, from: "Geometry and topology (Athens, Ga., 1985)" (editors C McCrory, T Shifrin), Lecture Notes in Pure and Appl. Math. 105, Dekker (1987) 233 MR873296
39	F Quinn, Homotopically stratified sets, J. Amer. Math. Soc. 1 (1988) 441 MR928266
40	M Saralegi-Aranguren, Cohomologie d'intersection des actions toriques simples, Indag. Math. $($N.S.$)$ 7 (1996) 389 MR1621397
41	M Saralegi-Aranguren, de Rham intersection cohomology for general perversities, Illinois J. Math. 49 (2005) 737 MR2210257
42	P H Siegel, Witt spaces: a geometric cycle theory for $K\mathrm{O}$–homology at odd primes, Amer. J. Math. 105 (1983) 1067 MR714770
43	S Weinberger, Group actions and higher signatures. II, Comm. Pure Appl. Math. 40 (1987) 179 MR872383
44	S Weinberger, The topological classification of stratified spaces, Chicago Lectures in Math., Univ. of Chicago Press (1994) MR1308714
45	S Weinberger, M Yan, Equivariant periodicity for abelian group actions, Adv. Geom. 1 (2001) 49 MR1823952
46	S Weinberger, M Yan, Equivariant periodicity for compact group actions, Adv. Geom. 5 (2005) 363 MR2154831
47	M Yan, The periodicity in stable equivariant surgery, Comm. Pure Appl. Math. 46 (1993) 1013 MR1223661