Geodesic
Rational Models of the Complement of a Subpolyhedron in a Manifold with Boundary
Canadian journal of mathematics, Tome 70 (2018) no. 2, pp. 265-293

Voir la notice de l'article provenant de la source Cambridge University Press

Let $W$ be a compact simply connected triangulated manifold with boundary and let $K\,\subset \,W$ be a subpolyhedron. We construct an algebraic model of the rational homotopy type of $W\text{ }\!\!\backslash\!\!\text{ K}$ out of a model of the map of pairs $\left( K,\,K\cap \partial W \right)\,\to \,\left( W,\,\partial W \right)$ under some high codimension hypothesis.We deduce the rational homotopy invariance of the configuration space of two points in a compactmanifold with boundary under 2-connectedness hypotheses. Also, we exhibit nice explicit models of these configuration spaces for a large class of compact manifolds.
DOI : 10.4153/CJM-2017-021-3
Mots-clés : 55P62, 55R80, Lefschetz duality, Sullivan model, configuration space 
Bulens, Hector Cordova; Lambrechts, Pascal; Stanley, Don. Rational Models of the Complement of a Subpolyhedron in a Manifold with Boundary. Canadian journal of mathematics, Tome 70 (2018) no. 2, pp. 265-293. doi: 10.4153/CJM-2017-021-3
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[1] [1] Cohen, F. R. and Taylor, L. R., Configuration spaces: applications to Gelfand-Fuks cohomology. Bull. Amer. Math. Soc. 84(1978), no. 1, 134–136. Google Scholar | DOI

[2] [2] Cordova Bulens, H., Rational model of the configuration space of two points in a simply connected closed manifold. Proc. Amer. Math. Soc. 143(2015), no. 12, 5437–5453. http://dx.doi.Org/10.1090/proc/12666 Google Scholar

[3] [3] Cordova Bulens, H., Lambrechts, P., and Stanley, D., Pretty rational models for Poincaré duality pairs. http://arxiv:1505.04818 Google Scholar

[4] [4] Curtis, E. B., Simplicial homotopy theory. Advances in Math. 6(1971), 107–209. http://dx.doi.Org/10.1016/0001-8708(71)90015-6 Google Scholar

[5] [5] Félix, Y., Halperin, S., and Thomas, J.-C., Rational homotopy theory. Graduate Texts in Mathematics , 205, Springer-Verlag, New York, 2001. http://dx.doi.Org/10.1007/978-1-4613-0105-9 Google Scholar

[6] [6] Hudson, J. F. P., Piecewise linear topology. University of Chicago Lecture Notes prepared with the assistance of J. L. Shaneson and J. Lees , W. A. Benjamin, Inc., New York-Amsterdam, 1969. Google Scholar

[7] [7] Lambrechts, P. and Stanley, D., The rational homotopy type of configuration spaces of two points. Ann. Inst. Fourier (Grenoble) 54(2004), no. 4, 1029–1052. http://dx.doi.Org/10.58O2/aif.2O42 Google Scholar

[8] [8] Lambrechts, P. and Stanley, D., Algebraic models of Poincaré embeddings. Algebr. Geom. Topol. 5(2005), 135–182. http://dx.doi.Org/10.2140/agt.2005.5.135 Google Scholar

[9] [9] Lambrechts, P. and Stanley, D., Poincaré duality and commutative differential graded algebras. Ann. Sci. ác. Norm. Super. (4) 41(2008), no. 4, 495–509. Google Scholar

[10] [10] Lambrechts, P. and Stanley, D., A remarkable DGmodule model for configuration spaces. Algebr. Geom. Topol. 8(2008), no. 2, 1191–1222. http://dx.doi.Org/10.2140/agt.2008.8.1191 Google Scholar

[11] [11] Longoni, R. and Salvatore, P., Configuration spaces are not homotopy invariant. Topology 44(2005), no. 2, 375–380. http://dx.doi.Org/10.1016/j.top.2004.11.002 Google Scholar

[12] [12] Weibel, C. A., An introduction to homological algebra. Cambridge Studies in Advanced Mathematics , 38, Cambridge University Press, Cambridge, 1994. Google Scholar | DOI

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