[Homotopy boundaries and Quillen models]. A homotopy boundary of a finite simply connected CW-complex X is the boundary of a compact manifold of the homotopy type of X. We study the rational homotopy type of the homotopy boundaries of X using Quillen models and we show, in particular, that a large class of homotopy boundaries of X is rationally determined by the rational homotopy type of X.
Kahl, T., Lambrechts, P., & Vandembroucq, L. (2006). Bords homotopiques et modèles de Quillen. Homology, Homotopy and Applications, 8(2), 1-28. https://doi.org/10.4310/HHA.2006.v8.n2.a1 (Original work published 2006)