Skip to main content Accessibility help
×
Home

CONFIGURATION CATEGORIES AND HOMOTOPY AUTOMORPHISMS

  • MICHAEL S. WEISS (a1)

Abstract

Let M be a smooth compact manifold with boundary. Under some geometric conditions on M, a homotopical model for the pair (M, ∂M) can be recovered from the configuration category of M \ ∂M. The grouplike monoid of derived homotopy automorphisms of the configuration category of M \ ∂M then acts on the homotopical model of (M, ∂M). That action is compatible with a better known homotopical action of the homeomorphism group of M \ ∂M on (M, ∂M).

Copyright

References

Hide All
1.Andrade, R., From manifolds to invariants of En-algebras, PhD Thesis (MIT, 2010).
2.Adams, J. F., Infinite loop spaces, Annals of Mathematics Studies, vol. 90 (Princeton University Press, Princeton, NJ, 1978).10.1515/9781400821259
3.Boavida de Brito, P., Segal objects and the Grothendieck construction, in An Alpine bouquet of algebraic topology (Ausoni, C., Hess, K., Johnson, B., Moerdijk, I. and Scherer, J., Editors), Contemporary Mathematics, vol. 708 (American Mathematical Society, Providence, RI, 2018), 1944.
4.Boavida de Brito, P. and Weiss, M. S., Spaces of smooth embeddings and configuration categories, J. Topol. 11 (2018), 65143.
5.Dwyer, W. G. and Kan, D., Function complexes in homotopical algebra, Topology 19 (1980), 427440.
6.Hirschhorn, P. S., Model categories and their localizations, Mathematical Surveys and Monographs, vol. 99 (American Mathematical Society, Providence, RI, 2002).
7.Hovey, M., Model categories, Mathematical Surveys and Monographs, vol. 63 (American Mathematical Society, Providence, RI, 1999), xii+209.
8.Rezk, C., A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001), 9731007.
9.Segal, G., Categories and cohomology theories, Topology 13 (1974), 293312.10.1016/0040-9383(74)90022-6
10.Thomason, R. W., Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979), 91109.
11.Tillmann, S., Occupants in simplicial complexes, to appear in Alg. Geom. Topology.
12.Tillmann, S. and Weiss, M. S., Occupants in manifolds, in Manifolds and K-theory (Arone, G., Johnson, B., Lambrechts, P., Munson, B. A. and Volić, I., Editors), Contemporary Mathematics, vol. 682 (American Mathematical Society, Providence, RI, 2017).
13.Weiss, M., Dalian notes on Pontryagin classes, arXiv:1507.00153.

MSC classification

CONFIGURATION CATEGORIES AND HOMOTOPY AUTOMORPHISMS

  • MICHAEL S. WEISS (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed