To an inclusion H ⊂ G of topological groups, we associate a spectrum DH⊂G which coincides with the dualizing spectrum DG of Klein [Math. Ann. 319 (2001) 421-456] when H = G. We also introduce a fibered spectrum analogue.
The main application is to give a purely homotopy theoretic construction of Poincaré embeddings in stable codimension.
Klein, John R  1
@article{10_2140_agt_2007_7_109,
author = {Klein, John R},
title = {The dualizing spectrum {II}},
journal = {Algebraic and Geometric Topology},
pages = {109--133},
year = {2007},
volume = {7},
number = {1},
doi = {10.2140/agt.2007.7.109},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.109/}
}
Klein, John R. The dualizing spectrum II. Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 109-133. doi: 10.2140/agt.2007.7.109
[1] , , , , Finite loop spaces are manifolds, Acta Math. 192 (2004) 5
[2] , Poincaré duality embeddings and fiberwise homotopy theory, Topology 38 (1999) 597
[3] , Poincaré immersions, Forum Math. 11 (1999) 717
[4] , Poincaré duality spaces, from: "Surveys on surgery theory, Vol. 1", Ann. of Math. Stud. 145, Princeton Univ. Press (2000) 135
[5] , The dualizing spectrum of a topological group, Math. Ann. 319 (2001) 421
[6] , Embedding, compression and fiberwise homotopy theory, Algebr. Geom. Topol. 2 (2002) 311
[7] , Poincaré duality embeddings and fibrewise homotopy theory. II, Q. J. Math. 53 (2002) 319
[8] , , Algebraic models of Poincaré embeddings, Algebr. Geom. Topol. 5 (2005) 135
[9] , , , Embeddings up to homotopy of two-cones in Euclidean space, Trans. Amer. Math. Soc. 354 (2002) 3973
[10] , , Parametrized homotopy theory
[11] , A homotopy-theoretic proof of Williams's metastable Poincaré embedding theorem, Duke Math. J. 88 (1997) 435
[12] , Spectra in model categories and applications to the algebraic cotangent complex, J. Pure Appl. Algebra 120 (1997) 77
[13] , Spaces satisfying Poincaré duality, Topology 6 (1967) 77
[14] , The canonical involution on the algebraic $K$-theory of spaces, from: "Algebraic topology, Aarhus 1982 (Aarhus, 1982)", Lecture Notes in Math. 1051, Springer (1984) 156
[15] , Poincaré complexes. I, Ann. of Math. $(2)$ 86 (1967) 213
[16] , Surgery on compact manifolds, Mathematical Surveys and Monographs 69, American Mathematical Society (1999)
[17] , Applications of unstable normal invariants. I, Compositio Math. 38 (1979) 55
[18] , Hopf invariants, localization and embeddings of Poincaré complexes, Pacific J. Math. 84 (1979) 217
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