## The homotopy type of the space of diffeomorphisms. II

HTML articles powered by AMS MathViewer

- by Dan Burghelea and Richard Lashof
- Trans. Amer. Math. Soc.
**196**(1974), 37-50 - DOI: https://doi.org/10.1090/S0002-9947-74-99951-6
- PDF | Request permission

## Abstract:

The result (proved in Part I) that ${\operatorname {Diff}}({D^n},\partial ) \simeq {\Omega ^{n + 1}}({\text {PL}_n}/{O_n})$ is used to compute some new homotopy of ${\operatorname {Diff}}({D^n},\partial {D^n})$. The relation between smooth and PL pseudo-isotopy is explored. Known and new results on the homotopy of ${\text {PL}_n}$ are summarized.## References

- A. Haefliger and C. T. C. Wall,
*Piecewise linear bundles in the stable range*, Topology**4**(1965), 209–214. MR**184243**, DOI 10.1016/0040-9383(65)90007-8 - Glen E. Bredon,
*A $\Pi _\ast$-module structure for $\Theta _\ast$ and applications to transformation groups*, Ann. of Math. (2)**86**(1967), 434–448. MR**221518**, DOI 10.2307/1970609 - John Grier Miller,
*Homotopy groups of diffeomorphism groups*, Indiana Univ. Math. J.**24**(1974/75), 719–726. MR**362355**, DOI 10.1512/iumj.1975.24.24054 - William Browder,
*The Kervaire invariant of framed manifolds and its generalization*, Ann. of Math. (2)**90**(1969), 157–186. MR**251736**, DOI 10.2307/1970686 - M. G. Barratt and M. E. Mahowald,
*The metastable homotopy of $\textrm {O}(n)$*, Bull. Amer. Math. Soc.**70**(1964), 758–760. MR**182004**, DOI 10.1090/S0002-9904-1964-11229-5 - I. M. James,
*On the iterated suspension*, Quart. J. Math. Oxford Ser. (2)**5**(1954), 1–10. MR**61836**, DOI 10.1093/qmath/5.1.1 - Mark Mahowald,
*Some Whitehead products in $S^{n}$*, Topology**4**(1965), 17–26. MR**178467**, DOI 10.1016/0040-9383(65)90046-7
G. F. Paechter, - C. P. Rourke and B. J. Sanderson,
*Block bundles. I*, Ann. of Math. (2)**87**(1968), 1–28. MR**226645**, DOI 10.2307/1970591 - I. A. Volodin,
*Algebraic $K$-theory*, Uspehi Mat. Nauk**27**(1972), no. 4(166), 207–208 (Russian). MR**0393191**
—, - R. James Milgram,
*On the Haefliger knot groups*, Bull. Amer. Math. Soc.**78**(1972), 861–865. MR**315728**, DOI 10.1090/S0002-9904-1972-13062-3 - Alain Chenciner,
*Pseudo-isotopies différentiables et pseudo-isotopies linéaires par morceaux*, C. R. Acad. Sci. Paris Sér. A-B**270**(1970), A1312–A1315 (French). MR**267587** - Morris W. Hirsch,
*On tubular neighborhoods of piecewise linear and topological manifolds.*, Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967) Prindle, Weber & Schmidt, Boston, Mass., 1968, pp. 63–80. MR**0236933** - N. H. Kuiper and R. K. Lashof,
*Microbundles and bundles. II. Semisimplical theory*, Invent. Math.**1**(1966), 243–259. MR**216507**, DOI 10.1007/BF01452244 - G. Brumfiel,
*On the homotopy groups of $\textrm {BPL}$ and $\textrm {PL/O}$*, Ann. of Math. (2)**88**(1968), 291–311. MR**234458**, DOI 10.2307/1970576

*The groups*${\pi _r}({V_{n,m}})$. I, II, III, IV, Quart. J. Math. Oxford Ser. (2)

**7**(1956), 249-268; ibid.

**9**(1958), 8-27;

**10**(1959), 17-37; 241-260. MR

**24**#A1725;

**25**#4540; #4541; #4542.

*Generalized Whitehead groups and pseudo-isotopy*, Uspehi Mat. Nauk (to appear).

## Bibliographic Information

- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**196**(1974), 37-50 - MSC: Primary 57E05; Secondary 58D05
- DOI: https://doi.org/10.1090/S0002-9947-74-99951-6