Intersection Spaces, Equivariant Moore Approximation and the Signature
Journal of Singularities, Tome 16 (2017), pp. 141-179
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We generalize the first author's construction of intersection spaces to the case of stratified pseudomanifolds of stratification depth 1 with twisted link bundles, assuming that each link possesses an equivariant Moore approximation for a suitable choice of structure group. As a by-product, we find new characteristic classes for fiber bundles admitting such approximations. For trivial bundles and flat bundles whose base has finite fundamental group these classes vanish. For oriented closed pseudomanifolds, we prove that the reduced rational cohomology of the intersection spaces satisfies global Poincar\'e duality across complementary perversities if the characteristic classes vanish. The signature of the intersection spaces agrees with the Novikov signature of the top stratum. As an application, these methods yield new results about the Goresky-MacPherson intersection homology signature of pseudomanifolds. We discuss several nontrivial examples, such as the case of flat bundles and symplectic toric manifolds.
@article{10_5427_jsing_2017_16g,
author = {Markus Banagl and Bryce Chriestenson},
title = {Intersection {Spaces,} {Equivariant} {Moore} {Approximation} and the {Signature}},
journal = {Journal of Singularities},
pages = {141--179},
publisher = {mathdoc},
volume = {16},
year = {2017},
doi = {10.5427/jsing.2017.16g},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2017.16g/}
}
TY - JOUR AU - Markus Banagl AU - Bryce Chriestenson TI - Intersection Spaces, Equivariant Moore Approximation and the Signature JO - Journal of Singularities PY - 2017 SP - 141 EP - 179 VL - 16 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2017.16g/ DO - 10.5427/jsing.2017.16g ID - 10_5427_jsing_2017_16g ER -
%0 Journal Article %A Markus Banagl %A Bryce Chriestenson %T Intersection Spaces, Equivariant Moore Approximation and the Signature %J Journal of Singularities %D 2017 %P 141-179 %V 16 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2017.16g/ %R 10.5427/jsing.2017.16g %F 10_5427_jsing_2017_16g
Markus Banagl; Bryce Chriestenson. Intersection Spaces, Equivariant Moore Approximation and the Signature. Journal of Singularities, Tome 16 (2017), pp. 141-179. doi: 10.5427/jsing.2017.16g
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