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Book Review

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Book Information:

Author: Shmuel Weinberger
Title: The topological classification of stratified spaces
Additional book information: Chicago Lectures in Math., Univ. of Chicago Press, Chicago, IL, 1994, xiv+283 pp., ISBN 0-226-88566-6, $47.50$

Douglas R. Anderson, Francis X. Connolly, Steven C. Ferry, and Erik K. Pedersen, Algebraic $K$-theory with continuous control at infinity, J. Pure Appl. Algebra 94 (1994), no. 1, 25–47. MR 1277522, DOI 10.1016/0022-4049(94)90004-3

Douglas R. Anderson and W. C. Hsiang, The functors $K_{-i}$ and pseudo-isotopies of polyhedra, Ann. of Math. (2) 105 (1977), no. 2, 201–223. MR 440573, DOI 10.2307/1970997

A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966

William Browder, Surgery on simply-connected manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 65, Springer-Verlag, New York-Heidelberg, 1972. MR 0358813

William Browder and Frank Quinn, A surgery theory for $G$-manifolds and stratified sets, Manifolds—Tokyo 1973 (Proc. Internat. Conf., Tokyo, 1973) Univ. Tokyo Press, Tokyo, 1975, pp. 27–36. MR 0375348

Sylvain E. Cappell and Julius L. Shaneson, Nonlinear similarity, Ann. of Math. (2) 113 (1981), no. 2, 315–355. MR 607895, DOI 10.2307/2006986

Sylvain E. Cappell and Julius L. Shaneson, Stratifiable maps and topological invariants, J. Amer. Math. Soc. 4 (1991), no. 3, 521–551. MR 1102578, DOI 10.1090/S0894-0347-1991-1102578-4

Sylvain Cappell, Julius Shaneson, and Shmuel Weinberger, Classes topologiques caractéristiques pour les actions de groupes sur les espaces singuliers, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 5, 293–295 (French, with English summary). MR 1126399

Sylvain Cappell and Shmuel Weinberger, A simple construction of Atiyah-Singer classes and piecewise linear transformation groups, J. Differential Geom. 33 (1991), no. 3, 731–742. MR 1100209

Sylvain Cappell and Shmuel Weinberger, Classification de certains espaces stratifiés, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 6, 399–401 (French, with English summary). MR 1126422

Steve Ferry, Homotoping $\varepsilon$-maps to homeomorphisms, Amer. J. Math. 101 (1979), no. 3, 567–582. MR 533191, DOI 10.2307/2373798

Steven C. Ferry, Andrew Ranicki, and Jonathan Rosenberg (eds.), Novikov conjectures, index theorems and rigidity. Vol. 2, London Mathematical Society Lecture Note Series, vol. 227, Cambridge University Press, Cambridge, 1995. Including papers from the conference held at the Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, September 6–10, 1993. MR 1388306

Steven C. Ferry, Andrew Ranicki, and Jonathan Rosenberg (eds.), Novikov conjectures, index theorems and rigidity. Vol. 1, London Mathematical Society Lecture Note Series, vol. 226, Cambridge University Press, Cambridge, 1995. Including papers from the conference held at the Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, September 6–10, 1993. MR 1388294

Mark Goresky and Robert MacPherson, Intersection homology theory, Topology 19 (1980), no. 2, 135–162. MR 572580, DOI 10.1016/0040-9383(80)90003-8

W. C. Hsiang and William Pardon, When are topologically equivalent orthogonal transformations linearly equivalent?, Invent. Math. 68 (1982), no. 2, 275–316. MR 666164, DOI 10.1007/BF01394060

Bruce Hughes, Geometric topology of stratified spaces, Electron. Res. Announc. Amer. Math. Soc. 2 (1996), no. 2, 73–81. MR 1412945, DOI 10.1090/S1079-6762-96-00010-8

[HTWW]

B. Hughes, L. Taylor, S. Weinberger, and B. Williams, Neighborhoods in stratified spaces with two strata (preprint).

Ib Madsen and Mel Rothenberg, On the classification of $G$-spheres, Proceedings of the Northwestern Homotopy Theory Conference (Evanston, Ill., 1982) Contemp. Math., vol. 19, Amer. Math. Soc., Providence, RI, 1983, pp. 193–226. MR 711053, DOI 10.1090/conm/019/711053

Frank Quinn, Homotopically stratified sets, J. Amer. Math. Soc. 1 (1988), no. 2, 441–499. MR 928266, DOI 10.1090/S0894-0347-1988-0928266-2

Frank Quinn, Ends of maps. I, Ann. of Math. (2) 110 (1979), no. 2, 275–331. MR 549490, DOI 10.2307/1971262

A. A. Ranicki, Algebraic $L$-theory and topological manifolds, Cambridge Tracts in Mathematics, vol. 102, Cambridge University Press, Cambridge, 1992. MR 1211640

[R]

M. Rothenberg, Review of Equivariant surgery theories and their periodicity properties by K.H. Dovermann and R. Schultz, BAMS 28 (1993) 375-382.

Jonathan Rosenberg and Shmuel Weinberger, Higher $G$-signatures for Lipschitz manifolds, $K$-Theory 7 (1993), no. 2, 101–132. MR 1235284, DOI 10.1007/BF00962083

Reinhard Schultz, On the topological classification of linear representations, Topology 16 (1977), no. 3, 263–269. MR 500964, DOI 10.1016/0040-9383(77)90007-6

Mark Steinberger, The equivariant topological $s$-cobordism theorem, Invent. Math. 91 (1988), no. 1, 61–104. MR 918237, DOI 10.1007/BF01404913

C. T. C. Wall, Surgery on compact manifolds, London Mathematical Society Monographs, No. 1, Academic Press, London-New York, 1970. MR 0431216

[We]

S. Weinberger, Review of Algebraic L-theory and topological manifolds by A. Ranicki, BAMS 33 (1996) 93-99.

Review Information:

Reviewer: Sylvain Cappell
Affiliation: New York University
Email: cappell@cappell.cims.nyu.edu