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

Volume 26
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Bundle transfer of $L$–homology orientation classes for singular spaces

Markus Banagl

Algebraic & Geometric Topology 24 (2024) 2579–2618
Bibliography
1 M Banagl, Extending intersection homology type invariants to non-Witt spaces, 760 (2002) MR1937924
2 M Banagl, The L–class of non-Witt spaces, Ann. of Math. 163 (2006) 743 MR2215133
3 M Banagl, Topological invariants of stratified spaces, Springer (2007) MR2286904
4 M Banagl, Topological and Hodge L–classes of singular covering spaces and varieties with trivial canonical class, Geom. Dedicata 199 (2019) 189 MR3928798
5 M Banagl, Gysin restriction of topological and Hodge-theoretic characteristic classes for singular spaces, New York J. Math. 26 (2020) 1273 MR4180225
6 M Banagl, Transfer and the spectrum-level Siegel–Sullivan KO–orientation for singular spaces, preprint (2023) arXiv:2305.06045
7 M Banagl, G Laures, J E McClure, The L–homology fundamental class for IP–spaces and the stratified Novikov conjecture, Selecta Math. 25 (2019) 7 MR3908854
8 J C Becker, D H Gottlieb, The transfer map and fiber bundles, Topology 14 (1975) 1 MR0377873
9 J M Boardman, Stable homotopy theory, V: Duality and Thom spectra, mimeographed notes (1966)
10 J F de Bobadilla, I Pallarés, The Brasselet–Schürmann–Yokura conjecture on L–classes of singular varieties, preprint (2020) arXiv:2007.11537
11 J P Brasselet, J Schürmann, S Yokura, Hirzebruch classes and motivic Chern classes for singular spaces, J. Topol. Anal. 2 (2010) 1 MR2646988
12 S Buoncristiano, C P Rourke, B J Sanderson, A geometric approach to homology theory, 18, Cambridge Univ. Press (1976) MR0413113
13 S Cappell, S Weinberger, Classification de certains espaces stratifiés, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991) 399 MR1126422
14 S Carmeli, B Cnossen, M Ramzi, L Yanovski, Characters and transfer maps via categorified traces, preprint (2023) arXiv:2210.17364v2
15 A J Casson, Generalisations and applications of block bundles, from: "The Hauptvermutung book", K–Monogr. Math. 1, Kluwer Academic (1996) 33 MR1434102
16 J Cheeger, Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18 (1983) 575 MR0730920
17 M M Cohen, A general theory of relative regular neighborhoods, Trans. Amer. Math. Soc. 136 (1969) 189 MR0248802
18 S J Curran, Intersection homology and free group actions on Witt spaces, Michigan Math. J. 39 (1992) 111 MR1137893
19 J Ebert, O Randal-Williams, Generalised Miller–Morita–Mumford classes for block bundles and topological bundles, Algebr. Geom. Topol. 14 (2014) 1181 MR3180831
20 G Friedman, Singular intersection homology, 33, Cambridge Univ. Press (2020) MR4406774
21 M Goresky, R MacPherson, Intersection homology theory, Topology 19 (1980) 135 MR0572580
22 M Goresky, R MacPherson, Intersection homology, II, Invent. Math. 72 (1983) 77 MR0696691
23 M Goresky, R MacPherson, Stratified Morse theory, 14, Springer (1988) MR0932724
24 M Goresky, P Siegel, Linking pairings on singular spaces, Comment. Math. Helv. 58 (1983) 96 MR0699009
25 F Hebestreit, M Land, W Lück, O Randal-Williams, A vanishing theorem for tautological classes of aspherical manifolds, Geom. Topol. 25 (2021) 47 MR4226228
26 W C Hsiang, C T C Wall, Orientability of manifolds for generalised homology theories, Trans. Amer. Math. Soc. 118 (1965) 352 MR0177407
27 F Kirwan, J Woolf, An introduction to intersection homology theory, Chapman & Hall (2006) MR2207421
28 J R Klein, C Malkiewich, M Ramzi, On the multiplicativity of the Euler characteristic, Proc. Amer. Math. Soc. 151 (2023) 4997 MR4634901
29 N H Kuiper, R K Lashof, Microbundles and bundles, I : Elementary theory, Invent. Math. 1 (1966) 1 MR0216506
30 M Land, T Nikolaus, On the relation between K– and L–theory of C–algebras, Math. Ann. 371 (2018) 517 MR3788857
31 G Laures, J E McClure, Multiplicative properties of Quinn spectra, Forum Math. 26 (2014) 1117 MR3228927
32 W Lück, A Ranicki, Surgery obstructions of fibre bundles, J. Pure Appl. Algebra 81 (1992) 139 MR1176019
33 I Madsen, R J Milgram, The classifying spaces for surgery and cobordism of manifolds, 92, Princeton Univ. Press (1979) MR0548575
34 L Maxim, J Schürmann, Characteristic classes of mixed Hodge modules and applications, from: "Schubert varieties, equivariant cohomology and characteristic classes" (editors J Buczyński, M Michałek, E Postinghel), Eur. Math. Soc. (2018) 159 MR3754192
35 J W Morgan, D P Sullivan, The transversality characteristic class and linking cycles in surgery theory, Ann. of Math. 99 (1974) 463 MR0350748
36 W L Pardon, Intersection homology Poincaré spaces and the characteristic variety theorem, Comment. Math. Helv. 65 (1990) 198 MR1057240
37 A Ranicki, The total surgery obstruction, from: "Algebraic topology" (editors J L Dupont, I H Madsen), Lecture Notes in Math. 763, Springer (1979) 275 MR0561227
38 A Ranicki, Exact sequences in the algebraic theory of surgery, 26, Princeton Univ. Press (1981) MR0620795
39 A A Ranicki, Algebraic L–theory and topological manifolds, 102, Cambridge Univ. Press (1992) MR1211640
40 C P Rourke, Block structures in geometric and algebraic topology, from: "Actes du Congrès International des Mathématiciens" (editors M Berger, J Dieudonné, J Leray, J L Lions, P Malliavin, J P Serre), Gauthier-Villars (1971) 127 MR0420642
41 C P Rourke, B J Sanderson, Block bundles, I, Ann. of Math. 87 (1968) 1 MR0226645
42 Y B Rudyak, On Thom spectra, orientability, and cobordism, Springer (1998) MR1627486
43 J Schürmann, Specialization of motivic Hodge–Chern classes, preprint (2009) arXiv:0909.3478
44 P H Siegel, Witt spaces : a geometric cycle theory for KO–homology at odd primes, Amer. J. Math. 105 (1983) 1067 MR0714770
45 D Sullivan, Geometric topology, I: Localization, periodicity, and Galois symmetry, Massachusetts Institute of Technology (1970) MR494074
46 R M Switzer, Algebraic topology: homotopy and homology, 212, Springer (1975) MR0385836
47 L Taylor, B Williams, Surgery spaces: formulae and structure, from: "Algebraic topology" (editors P Hoffman, V Snaith), Lecture Notes in Math. 741, Springer (1979) 170 MR0557167
48 R Thom, Les classes caractéristiques de Pontrjagin des variétés triangulées, from: "Symposium internacional de topología algebraica", Universidad Nacional Autónoma de México and UNESCO (1958) 54 MR0102071
49 S Weinberger, The topological classification of stratified spaces, Univ. of Chicago Press (1994) MR1308714
50 R E Williamson Jr., Cobordism of combinatorial manifolds, Ann. of Math. 83 (1966) 1 MR0184242