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Book Review

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Book Information:

Author: V. A. Vassiliev
Title: Complements of discriminants of smooth maps: Topology and applications
Additional book information: American Mathematical Society, Providence, RI, 1992, 208 pp., US$164.00. ISBN 0-8218-4555-1.

References [Enhancements On Off] (What's this?)

  • [An] D. W. Anderson, A generalization of the Eilenberg-Moore spectral sequence, Bull. Amer. Math. Soc. 78 (1972), 784-788. MR 0310889 (46:9987)
  • [AK] S. Araki and T. Kudo, The topology of H-spaces and H-squaring operations, Mem. Fac. Sci. Kyushu Univ. Ser. A (1956), 85-120. MR 0087948 (19:442b)
  • [A1] V. I. Arnol'd, The cohomology ring of the colored braid group, Mat. Zametki 2 (1969), 247-248. MR 0242196 (39:3529)
  • [A2] -, On a class of algebraic functions and cohomology of swallow tails, Uspekhi Mat. Nauk 23 (1968), 247-248.
  • [A3] -, Topological invariants of algebraic functions, Funktsional Anal. i Prilozhen 4 (1970), 1-9; English transl. in Functional Anal. Appl. 4 (1970). MR 0276244 (43:1991)
  • [BG] M. Bendersky and S. Gitler, The cohomology of certain function spaces, Trans. Amer. Math. Soc. 326 (1991), 423-440. MR 1010881 (92d:55005)
  • [BL] J. Birman and X. S. Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993), 225-270. MR 1198809 (94d:57010)
  • [B] C.-F. Bödigheimer, Stable splittings of mapping spaces, Algebraic Topology (H. Miller and D. Ravenel, eds.), Lecture Notes in Math., vol. 1286, Springer-Verlag, New York, 1987, pp. 174-187. MR 922926 (89c:55011)
  • [BCM] C.-F. Bödigheimer, F. R. Cohen, and R. J. Milgram, Truncated symmetric products and configuration spaces, Math. Z. 214 (1993), 179-286. MR 1240884 (95a:55043)
  • [BCT] C.-F. Bödigheimer, F. R. Cohen, and L. R. Taylor, On the homology of configuration spaces, Topology 28 (1989), 111-123. MR 991102 (90h:57031)
  • [C1] F. R. Cohen, The homology of $ {{\mathcal{C}}_{n + 1}}$ spaces, Lecture Notes in Math., vol. 533, Springer-Verlag, New York, 1976, pp. 207-351; Bull. Amer. Math. Soc. 79 (1973), 761-764, 1236-1241. MR 0339176 (49:3939)
  • [C2] -, Artin's braid groups, classical homotopy theory and sundry other curiosities, Braids (Joan S. Birman and Anatoly Libgober, eds.), Contemp. Math., vol. 78, Amer. Math. Soc., Providence, RI, 1988, pp. 167-206.
  • [C3] -, The hyperelliptic mapping class groups $ {\text{SO(3)}}$ and $ \mathrm{Spin}^c(3)$, Amer. J. Math. 115 (1993), 389-434. MR 1216436 (94k:57021)
  • [CCMM] F. R. Cohen, R. Cohen, B. Mann, and J. Milgram, The topology of spaces of rational functions and divisors of surfaces, Acta Math. 166 (1991), 163-221. MR 1097023 (92k:55011)
  • [CT] F. R. Cohen and L. R. Taylor, Computations of Gelfand-Fuks cohomology, the cohomology of function spaces, and the cohomology of configuration spaces, Lecture Notes in Math., vol. 657, Springer-Verlag, New York, 1978, pp. 106-143. MR 513543 (80f:58050)
  • [DL] E. Dyer and R. Lashof, Homology of iterated loop spaces, Amer. J. Math. 84 (1962), 35-88. MR 0141112 (25:4523)
  • [FN] E. Fadell and L. Neuwirth, Configuration spaces, Math. Scand. 10 (1962), 111-118. MR 0141126 (25:4537)
  • [FxN] R. Fox and L. Neuwirth, The braid groups, Math. Scand. 10 (1962), 119-126. MR 0150755 (27:742)
  • [F] D. Fuks, Cohomology of the braid groups mod 2, Funktsional. Anal. i Prilozhen. 4 (1970), 143-151; English transl. in Functional Anal. Appl. 4 (1970). MR 0274463 (43:226)
  • [K] Y. Kamiyama, The modulo 2 homology groups of the space of rational functions, Osaka J. Math. 28 (1991), 229-242. MR 1132162 (92i:58031)
  • [L] V. Ya Lin, Artin's braids and related groups and spaces, J. Soviet Math. 18 (1979), 159-227. MR 584570 (82h:20047)
  • [LM] P. Löffler and J. Milgram, The structure of deleted symmetric products, Braids (Joan S. Birman and Anatoly Libgober, eds.), Contemp. Math., vol. 78, Amer. Math. Soc., Providence, RI, 1988, pp. 415-424. MR 975092 (90e:55033)
  • [Ma] J. P. May, The geometry of iterated loop spaces, Lecture Notes in Math., vol. 268, Springer-Verlag, New York, 1972. MR 0420610 (54:8623b)
  • [Mc] D. McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975), 91-107. MR 0358766 (50:11225)
  • [N] M. Nakaoka, Homology of the infinite symmetric group, Ann. of Math. (2) 73 (1961), 229-257. MR 0131874 (24:A1721)
  • [Se1] G. Segal, Configuration spaces and iterated loop spaces, Invent. Math. 21 (1973), 213-221. MR 0331377 (48:9710)
  • [Se2] -, Topology of spaces of rational functions, Acta. Math. 143 (1979), 39-72. MR 533892 (81c:55013)
  • [S] A. Shapiro, Obstructions to the imbedding of a complex in a euclidean space, I. The first obstruction, Ann. of Math. (2) 66 (1957), 256-269. MR 0089410 (19:671a)
  • [Sm] S. Smale, On the topology of algorithms. I, J. Complexity 3 (1987), 81-89. MR 907191 (89f:68020)
  • [V] F. V. Vainshtein, Cohomology of the braid groups, Funktsional. Anal. i Prilozen. 12 (1978), 72-73; English transl. in Functional Anal. Appl. 12 (1978). MR 498903 (80g:32019)
  • [W] Wu Wen-Tsün, A theory of imbedding, immersion, and isotopy of polytopes in a Euclidean space, Science Press, Beijing, 1974.

Review Information:

Reviewer: Frederick R. Cohen
Journal: Bull. Amer. Math. Soc. 31 (1994), 258-265
DOI: https://doi.org/10.1090/S0273-0979-1994-00525-7
American Mathematical Society