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Transactions of the American Mathematical Society

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The topology of resolution towers


Authors: Selman Akbulut and Henry King
Journal: Trans. Amer. Math. Soc. 302 (1987), 497-521
MSC: Primary 57R90; Secondary 14F45, 14G30
MathSciNet review: 891632
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Abstract: An obstruction theory is given to determine when a space has a resolution tower. This can be used to decide whether or not the space is homeomorphic to a real algebraic set.


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

  • [AK$ _{1}$] Selman Akbulut and Henry King, The topology of real algebraic sets, Enseign. Math. (2) 29 (1983), no. 3-4, 221–261. MR 719311
  • [AK$ _{2}$] -, Resolution tower.
  • [AK$ _{3}$] -, Resolution towers on real algebraic sets.
  • [AK$ _{4}$] -, Algebraic structures on resolution towers.
  • [AK$ _{5}$] -, The topological classification of $ 3$-dimensional real algebraic sets.
  • [AK$ _{6}$] Selman Akbulut and Henry C. King, The topology of real algebraic sets with isolated singularities, Ann. of Math. (2) 113 (1981), no. 3, 425–446. MR 621011, 10.2307/2006992
  • [AK$ _{7}$] -, Submanifolds and homology of nonsingular algebraic varieties, Amer. J. Math. (1985), 45-83.
  • [AK$ _{8}$] Selman Akbulut and Henry C. King, Real algebraic structures on topological spaces, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 79–162. MR 623536
  • [AT] Selman Akbulut and Laurence Taylor, A topological resolution theorem, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 163–195. MR 623537
  • [D] D. Sullivan, Singularities in spaces, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Springer, Berlin, 1971, pp. 196–206. Lecture Notes in Math., Vol. 209. MR 0339241

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0891632-3
Keywords: Stratified, resolutions
Article copyright: © Copyright 1987 American Mathematical Society