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Pretty rational models for Poincaré duality pairs. (English) Zbl 1417.55013
In an earlier paper [P. Lambrechts and D. Stanley, Ann. Sci. Éc. Norm. Supér. (4) 41, No. 4, 497–511 (2008; Zbl 1172.13009)], two of the authors of this paper showed that when $$X$$ is a simply connected Poincaré duality space one can construct a commutative differential graded algebra (CDGA) model whose underlying algebra satisfies Poincaré duality. The goal of this paper is to extend the result to the case of pairs. The aim is to produce a CDGA morphism between two CDGAs representing each element of the pair. More specifically the authors show that many Poincaré duality pairs admit what the authors call pretty models. This somewhat technical definition covers in particular even-dimensional disk bundles over a simply connected closed manifold relative to their sphere bundles, and the complement of a subpolyhedron of high codimension in a closed manifold relative to its natural boundary.
##### MSC:
 55P62 Rational homotopy theory 55M05 Duality in algebraic topology
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##### References:
 [1] 10.4153/CJM-2017-021-3 · Zbl 1388.55010 [2] 10.1007/978-1-4613-0105-9 [3] 10.24033/bsmf.2558 · Zbl 1160.55006 [4] 10.5802/aif.2042 · Zbl 1069.55006 [5] 10.2140/agt.2005.5.135 · Zbl 1114.55007 [6] 10.24033/asens.2074 · Zbl 1172.13009 [7] 10.2140/agt.2008.8.1191 · Zbl 1152.55004 [8] 10.1007/BF02684341 · Zbl 0374.57002 [9] 10.2307/1970688 · Zbl 0153.25401
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