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2005 Algebraic models of Poincaré embeddings
Pascal Lambrechts, Donald Stanley
Algebr. Geom. Topol. 5(1): 135-182 (2005). DOI: 10.2140/agt.2005.5.135


Let f:PW be an embedding of a compact polyhedron in a closed oriented manifold W, let T be a regular neighborhood of P in W and let C:=W\T¯ be its complement. Then W is the homotopy push-out of a diagram CTP. This homotopy push-out square is an example of what is called a Poincaré embedding.

We study how to construct algebraic models, in particular in the sense of Sullivan, of that homotopy push-out from a model of the map f. When the codimension is high enough this allows us to completely determine the rational homotopy type of the complement CW\f(P). Moreover we construct examples to show that our restriction on the codimension is sharp.

Without restriction on the codimension we also give differentiable modules models of Poincaré embeddings and we deduce a refinement of the classical Lefschetz duality theorem, giving information on the algebra structure of the cohomology of the complement.


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Pascal Lambrechts. Donald Stanley. "Algebraic models of Poincaré embeddings." Algebr. Geom. Topol. 5 (1) 135 - 182, 2005.


Received: 8 May 2003; Revised: 18 August 2004; Accepted: 21 September 2004; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1114.55007
MathSciNet: MR2135550
Digital Object Identifier: 10.2140/agt.2005.5.135

Primary: 55P62
Secondary: 55M05, 57Q35

Rights: Copyright © 2005 Mathematical Sciences Publishers


Vol.5 • No. 1 • 2005
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