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

Volume 26
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