© 2008 London Mathematical Society
Multiple disjunction for spaces of Poincaré embeddings
Brown University, Providence, RI 02912, USA tomg@math.brown.edu
Wayne State University, Detroit, MI 48202, USA klein@math.wayne.edu
We obtain multirelative connectivity statements about spaces of Poincaré embeddings, as precursors to analogous statements about spaces of smooth embeddings. The latter are the key to convergence results in the functor calculus approach to spaces of embeddings.
Received January 25, 2008.
2000 Mathematics Subject Classification 57N35 (primary), 57P10 (secondary)
Both authors are partially supported by the National Science Foundation.
References
- Dwyer W. G., Kan D. M. A classification theorem for diagrams of simplicial sets. Topology (1984) 23:139–155.[CrossRef][Web of Science]
- Goodwillie T. G. A multiple disjunction lemma for smooth concordance embeddings. Memoirs of the American Mathematical Society 86. (American Mathematical Society, 1990).
- Goodwillie T. G. Calculus. II. Analytic functors. K-Theory (1991/92) 5:295–332.
- Goodwillie T. G. Calculus III: Taylor series. Geom. Topol. (2003) 7:645–711.[CrossRef]
- Goodwillie T. G., Klein J. R. Multiple disjunction for spaces of smooth embeddings. (work in progress).
- Goodwillie T. G., Klein J. R., Weiss M. S. Spaces of smooth embeddings, disjunction and surgery. Surveys on surgery theory (2001) 2. Princeton, NJ: Princeton University Press. 221–284. Annals of Mathematics Studies 149.
- Goodwillie T. G., Weiss M. Embeddings from the point of view of immersion theory. I. Geom. Topol. (1999) 3:67–101.[CrossRef]
- Goodwillie T. G., Weiss M. Embeddings from the point of view of immersion theory. II. Geom. Topol. (1999) 3:103–118.[CrossRef]
- Klein J. R. Poincaré embeddings and fiberwise homotopy theory. Topology (1999) 38:597–620.[CrossRef][Web of Science]
- Quillen D. Homotopical algebra (1967) 43. Berlin–New York: Springer. Lecture Notes in Mathematics.
- Waldhausen F. Algebraic K-theory of spaces. Algebraic and geometric topology (1983) New Brunswick, N.J. 318–419. Lecture Notes in Math. 1126. (Springer, Berlin—New York, 1985).
- Weiss M. Calculus of embeddings. Bull. Amer. Math. Soc. (1996) 33:177–187.[CrossRef]
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