Brieskorn manifold explained

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

x ^{k _{1}} _{1} + … + x ^{k _{n}} _{n} =0 studied by .

Brieskorn manifolds give examples of exotic spheres.^{[1] [2]}

References

1. Greuel . Gert-Martin . Purkert . Walter . Walter Purkert. 2018 . Life and work of Egbert Brieskorn (1936 - 2013) . Journal of Singularities. 18. 1–28. 10.5427/jsing.2018.18a. 1711.09600. 3899530 . free. (See pp. 19–23.)
2. Book: van der Meer, J. W.. On the Construction and Classification of Exotic Structures on the 7-Sphere.

   Bachelor's thesis

   . 2017. Utrecht University.

• • • This book describes Brieskorn's work relating exotic spheres to singularities of complex manifolds.
• Book: Milnor, John. https://www.jstor.org/stable/j.ctt1b7x7xd.16 . Knots, Groups and 3-Manifolds: Papers Dedicated to the Memory of R.H. Fox. Lee P.. Neuwirth. On the 3-dimensional Brieskorn manifolds M(p,q,r) . John Milnor. Annals of Mathematics Studies. 84. 1975 . 175–225. . 978-0-691-08167-0. 0418127.