Brieskorn manifold: Difference between revisions
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==References== |
==References== |
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*{{citation |mr=0198497 |last=Brieskorn |first= Egbert V. | authorlink=Egbert Brieskorn |title=Examples of singular normal complex spaces which are topological manifolds |journal=[[Proceedings of the National Academy of Sciences]] |volume= 55|year= 1966|pages= 1395–1397 |issue=6 |doi=10.1073/pnas.55.6.1395 |pmc=224331 |pmid=16578636}} |
*{{citation |mr=0198497 |last=Brieskorn |first= Egbert V. | authorlink=Egbert Brieskorn |title=Examples of singular normal complex spaces which are topological manifolds |journal=[[Proceedings of the National Academy of Sciences]] |volume= 55|year= 1966|pages= 1395–1397 |issue=6 |doi=10.1073/pnas.55.6.1395 |pmc=224331 |pmid=16578636|doi-access=free }} |
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*{{citation |mr=0206972 |last=Brieskorn |first= Egbert | authorlink=Egbert Brieskorn |title=Beispiele zur Differentialtopologie von Singularitäten |journal=[[Inventiones Mathematicae]] |volume=2 |year=1966b |issue=1 |pages=1–14 |doi=10.1007/BF01403388}} |
*{{citation |mr=0206972 |last=Brieskorn |first= Egbert | authorlink=Egbert Brieskorn |title=Beispiele zur Differentialtopologie von Singularitäten |journal=[[Inventiones Mathematicae]] |volume=2 |year=1966b |issue=1 |pages=1–14 |doi=10.1007/BF01403388|s2cid=123268657 }} |
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*{{citation |first1=Friedrich |last1=Hirzebruch |authorlink1=Friedrich Hirzebruch |first2= Karl Heinz |last2=Mayer |title=O(n)-Mannigfaligkeiten, Exotische Sphären und Singularitäten |series= Lecture Notes in Mathematics |volume= 57 |publisher= [[Springer-Verlag]] |publication-place= Berlin-New York |year= 1968 |mr= 0229251 |doi=10.1007/BFb0074355}} This book describes Brieskorn's work relating exotic spheres to singularities of complex manifolds. |
*{{citation |first1=Friedrich |last1=Hirzebruch |authorlink1=Friedrich Hirzebruch |first2= Karl Heinz |last2=Mayer |title=O(n)-Mannigfaligkeiten, Exotische Sphären und Singularitäten |series= Lecture Notes in Mathematics |volume= 57 |publisher= [[Springer-Verlag]] |publication-place= Berlin-New York |year= 1968 |mr= 0229251 |doi=10.1007/BFb0074355|isbn=978-3-540-04227-3 }} This book describes Brieskorn's work relating exotic spheres to singularities of complex manifolds. |
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*{{Citation | last=Pham|first=Frédéric|authorlink=Frédéric Pham | title=Formules de Picard-Lefschetz généralisées et ramification des intégrales | mr=0195868 | year=1965 | journal=[[Bulletin de la Société Mathématique de France]] | issn=0037-9484 | volume=93 | pages=333–367}} |
*{{Citation | last=Pham|first=Frédéric|authorlink=Frédéric Pham | title=Formules de Picard-Lefschetz généralisées et ramification des intégrales | mr=0195868 | year=1965 | journal=[[Bulletin de la Société Mathématique de France]] | issn=0037-9484 | volume=93 | pages=333–367|doi=10.24033/bsmf.1628}} |
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[[Category:Singularity theory]] |
[[Category:Singularity theory]] |
Revision as of 10:30, 22 August 2021
In mathematics, a Brieskorn manifold or Brieskorn–Phạm manifold, introduced by Egbert Brieskorn (1966, 1966b), is the intersection of a small sphere around the origin with the singular hypersurface
studied by Frédéric 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, doi:10.1073/pnas.55.6.1395, MR 0198497, PMC 224331, PMID 16578636
- Brieskorn, Egbert (1966b), "Beispiele zur Differentialtopologie von Singularitäten", Inventiones Mathematicae, 2 (1): 1–14, doi:10.1007/BF01403388, MR 0206972, S2CID 123268657
- Hirzebruch, Friedrich; Mayer, Karl Heinz (1968), O(n)-Mannigfaligkeiten, Exotische Sphären und Singularitäten, Lecture Notes in Mathematics, vol. 57, Berlin-New York: Springer-Verlag, doi:10.1007/BFb0074355, ISBN 978-3-540-04227-3, MR 0229251 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, doi:10.24033/bsmf.1628, ISSN 0037-9484, MR 0195868