Singular decompositions of a cap product
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- by David Chataur, Martintxo Saralegi-Aranguren and Daniel Tanré PDF
- Proc. Amer. Math. Soc. 145 (2017), 3645-3656 Request permission
Abstract:
In the case of a compact orientable pseudomanifold, a well-known theorem of M. Goresky and R. MacPherson says that the cap product with a fundamental class factorizes through the intersection homology groups. In this work, we show that this classical cap product is compatible with a cap product in intersection (co)homology that we have previously introduced. If the pseudomanifold is also normal, for any commutative ring of coefficients, the existence of a classical Poincaré duality isomorphism is equivalent to the existence of an isomorphism between the intersection homology groups corresponding to the zero and the top perversities.References
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Additional Information
- David Chataur
- Affiliation: LAFMA, Université de Picardie Jules Verne, 33, rue Saint-Leu, 80039 Amiens Cedex 1, France
- MR Author ID: 657744
- Email: David.Chataur@u-picardie.fr
- Martintxo Saralegi-Aranguren
- Affiliation: Laboratoire de Mathématiques de Lens, EA 2462, Université d’Artois, SP18, rue Jean Souvraz, 62307 Lens Cedex, France
- MR Author ID: 238213
- Email: martin.saraleguiaranguren@univ-artois.fr
- Daniel Tanré
- Affiliation: Département de Mathématiques, UMR 8524, Université de Lille 1, 59655 Villeneuve d’Ascq Cedex, France
- MR Author ID: 205734
- Email: Daniel.Tanre@univ-lille1.fr
- Received by editor(s): June 14, 2016
- Received by editor(s) in revised form: September 21, 2016
- Published electronically: February 22, 2017
- Additional Notes: This research was supported through the program “Research in Pairs” at the Mathematisches Forschungsinstitut Oberwolfach in 2016. The authors thank the MFO for its generosity and hospitality.
The third author was also supported by the MINECO grant MTM2016-78647-P and the ANR-11-LABX-0007-01 “CEMPI” - Communicated by: Michael A. Mandell
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3645-3656
- MSC (2010): Primary 55N33, 57P10, 57N80
- DOI: https://doi.org/10.1090/proc/13508
- MathSciNet review: 3652815