Brieskorn manifold

In mathematics, a Brieskorn manifold or Brieskorn–Phạm manifold, introduced by Brieskorn (1966, 1966b), is the intersection of a small sphere around the origin with the singular hypersurface

x_{1}^{{k_{1}}}+\cdots +x_{n}^{{k_{n}}}=0

studied by Pham (1965).

Brieskorn manifolds give examples of exotic spheres.

References

Brieskorn, Egbert V. (1966), "Examples of singular normal complex spaces which are topological manifolds", Proceedings of the National Academy of Sciences, 55 (6): 1395–1397, MR 0198497, PMC 224331 , PMID 16578636, doi:10.1073/pnas.55.6.1395
Brieskorn, Egbert (1966b), "Beispiele zur Differentialtopologie von Singularitäten", Invent. Math., 2 (1): 1–14, MR 0206972, doi:10.1007/BF01403388
Hirzebruch, Friedrich; Mayer, Karl Heinz (1968), O(n)-Mannigfaligkeiten, Exotische Sphären und Singularitäten, Lecture Notes in Mathematics, 57, Berlin-New York: Springer-Verlag, MR 0229251, doi:10.1007/BFb0074355 This book describes Brieskorn's work relating exotic spheres to singularities of complex manifolds.
Pham, Frédéric (1965), "Formules de Picard-Lefschetz généralisées et ramification des intégrales", Bulletin de la Société Mathématique de France, 93: 333–367, ISSN 0037-9484, MR 0195868

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