Abstract
In this paper we assign, under reasonable hypothesis, to each pseudomanifold with isolated singularities a rational Poincaré duality space. These spaces are constructed with the formalism of intersection spaces defined by Markus Banagl and are indeed related to them in the even dimensional case.
Similar content being viewed by others
References
Akbulut, S., King, H.: The topology of real algebraic sets with isolated singularities. Ann. Math. 113, 425–446 (1981)
Banagl, M.: Intersection spaces, spatial homology truncation and string theory. Lecture Notes in Mathematics, vol. 1997. Springer, Berlin (2010)
Barge, J.: Structures différentiables sur les types d’homotopie rationnelle simplements connexes. Ann. Sci. Ec. Norm. Sup. 9, 469–501 (1976)
Browder, W.: Surgery on Simply-Connected Manifolds. Springer, Berlin (1972)
Dyer, M.: Rational homology and Whitehead products. Pac. J. Math. 40, 59–71 (1972)
Félix, Y., Halperin, S., Thomas, J.-C.: Rational Homotopy Theory. Vol. 205 Graduate Texts in Mathematics. Springer-Verlag, Berlin (2001)
Félix, Y., Oprea, J., Tanré, D.: Algebraic Models in Geometry, Oxford Graduate Texts in Mathemathics. Oxford University Press, Oxford (2008)
Goresky, M., MacPherson, R.: Intersection homology II. Invent. Math. 71, 77–129 (1983)
Goresky, M., MacPherson, R.: Intersection homology theory. Topology 19, 135–162 (1980)
Hirzebruch, F.: Topological Methods in Algebraic Geometry. Springer Verlag, Berlin (1966)
Klaus, S., Kreck, M.: A quick proof of the rational Hurewicz theorem and a computation of the rational homotopy groups of spheres. Math. Proc. Camb. Phil. Soc. 136, 617–623 (2004)
de Seguins Pazzis, C.: Invitation aux formes quadratiques. Calvage et Mounet, (2010)
Stasheff, J.: Rational Poincaré duality spaces. Ill. J. Math. 27, 104–109 (1983)
Strom, J.: Modern classical homotopy theory. Graduate Studies in Mathematics, vol. 127. American Mathematical Society, Providence (2011)
Sullivan, D.: Infinitesimal computations in topology. Inst. Hautes Etudes Sci. Publ. Math. 47, 269–331 (1977)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Klimczak, M. Poincaré duality for spaces with isolated singularities. manuscripta math. 153, 231–262 (2017). https://doi.org/10.1007/s00229-016-0884-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-016-0884-5