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On the index of a vector field at an isolated singularity

Research output: Chapter in book/report/conference proceedingConference contributionResearchpeer review

Authors

  • Wolfgang Ebeling
  • Sabir M. Gusein-Zade

Research Organisations

External Research Organisations

  • Lomonosov Moscow State University

Details

Original languageEnglish
Title of host publicationThe Arnoldfest
Subtitle of host publicationProceedings of a conference in honour of V. I. Arnold for his 60th birthday, Toronto, Canada, June 15-21, 1997.
EditorsEdward Bierstone, Boris Khesin, Askold G. Khovanskii, Jerold E. Marsden
Place of PublicationProvidence, Rhode Island
PublisherAmerican Mathematical Society
Pages141-152
Number of pages12
ISBN (print)978-0821809457
Publication statusPublished - 1999

Publication series

NameField Institute Communications
PublisherAmerican Mathematical Society
Volume24
ISSN (Print)1069-5265

Abstract

We consider manifolds with isolated singularities, i.e., topological spaces which are manifolds (say, C∞) outside discrete subsets (sets of singular points). For (germs of) manifolds with, so-called, cone-like singularities, a notion of the index of an isolated singular point of a vector field is introduced. There is given a formula for the index of a gradient vector field on a (real) isolated complete intersection singularity. The formula is in terms of signatures of certain quadratic forms on the corresponding spaces of thimbles

Cite this

On the index of a vector field at an isolated singularity. / Ebeling, Wolfgang; Gusein-Zade, Sabir M.
The Arnoldfest: Proceedings of a conference in honour of V. I. Arnold for his 60th birthday, Toronto, Canada, June 15-21, 1997.. ed. / Edward Bierstone; Boris Khesin; Askold G. Khovanskii; Jerold E. Marsden. Providence, Rhode Island: American Mathematical Society, 1999. p. 141-152 (Field Institute Communications; Vol. 24).

Research output: Chapter in book/report/conference proceedingConference contributionResearchpeer review

Ebeling, W & Gusein-Zade, SM 1999, On the index of a vector field at an isolated singularity. in E Bierstone, B Khesin, AG Khovanskii & JE Marsden (eds), The Arnoldfest: Proceedings of a conference in honour of V. I. Arnold for his 60th birthday, Toronto, Canada, June 15-21, 1997.. Field Institute Communications, vol. 24, American Mathematical Society, Providence, Rhode Island, pp. 141-152.
Ebeling, W., & Gusein-Zade, S. M. (1999). On the index of a vector field at an isolated singularity. In E. Bierstone, B. Khesin, A. G. Khovanskii, & J. E. Marsden (Eds.), The Arnoldfest: Proceedings of a conference in honour of V. I. Arnold for his 60th birthday, Toronto, Canada, June 15-21, 1997. (pp. 141-152). (Field Institute Communications; Vol. 24). American Mathematical Society.
Ebeling W, Gusein-Zade SM. On the index of a vector field at an isolated singularity. In Bierstone E, Khesin B, Khovanskii AG, Marsden JE, editors, The Arnoldfest: Proceedings of a conference in honour of V. I. Arnold for his 60th birthday, Toronto, Canada, June 15-21, 1997.. Providence, Rhode Island: American Mathematical Society. 1999. p. 141-152. (Field Institute Communications).
Ebeling, Wolfgang ; Gusein-Zade, Sabir M. / On the index of a vector field at an isolated singularity. The Arnoldfest: Proceedings of a conference in honour of V. I. Arnold for his 60th birthday, Toronto, Canada, June 15-21, 1997.. editor / Edward Bierstone ; Boris Khesin ; Askold G. Khovanskii ; Jerold E. Marsden. Providence, Rhode Island : American Mathematical Society, 1999. pp. 141-152 (Field Institute Communications).
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