Abstract
Partial configuration spaces are a version of ordinary configuration spaces where some points are allowed to coincide. We express these spaces as pullbacks of diagrams of ordinary configuration spaces and provide some examples where the limit coincides with the homotopy limit. We also indicate how one might use calculations in cohomology to show that the limit is the homotopy limit in general.
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References
Cohen, F.R.: Introduction to Configuration Spaces and Their Applications. Available at https://www.mimuw.edu.pl/~sjack/prosem/Cohen_Singapore.final.24.december.2008.pdf
Fadell, E., Neuwirth, L.: Configuration spaces. Math. Scand. 10, 111–118 (1962)
Goresky, M., MacPherson, R.: Stratified Morse theory. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) (Results in Mathematics and Related Areas (3)) 14. Springer, Berlin (1988)
Goodwillie, T.G., Munson, B.A.: A stable range description of the space of link maps. Algebr. Geom. Topol. 10, 1305–1315 (2010)
Goodwillie, T.G., Weiss, M.: Embeddings from the point of view of immersion theory II. Geom. Topol. 3, 103–118 (electronic) (1999)
Hirschhorn, P.S.: Model categories and their localizations. In: Mathematical Surveys and Monographs, vol. 99. American Mathematical Society, Providence, RI (2003)
Koschorke, U.: A generalization of Milnor’s \(\mu \)-invariants to higher-dimensional link maps. Topology 36(2), 301–324 (1997)
Klein, J., Williams, B.: Homotopical intersection theory, iii: Multirelative intersection problems. arXiv:1212.4420 (2012)
Munson, B.A.: A manifold calculus approach to link maps and the linking number. Algebr. Geom. Topol. 8(4), 2323–2353 (2008)
Munson, B.A., Volić, I.: Cosimplicial models for spaces of links. J. Homotopy Relat. Struct. 9(2), 419–454 (2014)
Munson, B.A., Volić, I.: Cubical homotopy theory. New Mathematical Monographs, Vol. 25. Cambridge University Press, Cambridge (2015)
Weiss, M.: Embeddings from the point of view of immersion theory I. Geom. Topol. 3, 67–101 (electronic) (1999)
Ziegler, G.M., Živaljević, R.T.: Homotopy types of subspace arrangements via diagrams of spaces. Math. Ann. 295(3), 527–548 (1993)
Acknowledgements
The authors would like to thank Franjo Šarčević for suggestions and corrections. The second author would like to thank the Simons Foundation for its support.
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Li, A.Q.H., Volić, I. (2021). Partial Configuration Spaces as Pullbacks of Diagrams of Configuration Spaces. In: Avdaković, S., Volić, I., Mujčić, A., Uzunović, T., Mujezinović, A. (eds) Advanced Technologies, Systems, and Applications V. IAT 2020. Lecture Notes in Networks and Systems, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-030-54765-3_1
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DOI: https://doi.org/10.1007/978-3-030-54765-3_1
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