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Forum Mathematicum

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Hrsg. v. Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Band 28, Heft 5

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Brieskorn manifolds, positive Sasakian geometry, and contact topology

Charles P. Boyer / Leonardo Macarini
  • Korrespondenzautor
  • Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária, Rio de Janeiro, Brazil, Postal Code 21941-909
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/ Otto van Koert
  • Department of Mathematics and Research Institute of Mathematics, Seoul National University, Building 27, room 402, San 56-1, Sillim-dong, Gwanak-gu, Seoul, South Korea, Postal Code 151-747
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Online erschienen: 20.11.2015 | DOI: https://doi.org/10.1515/forum-2015-0142

Abstract

Using S1-equivariant symplectic homology, in particular its mean Euler characteristic, of the natural filling of links of Brieskorn–Pham polynomials, we prove the existence of infinitely many inequivalent contact structures on various manifolds, including in dimension 5 the k-fold connected sums of S2×S3 and certain rational homology spheres. We then apply our result to show that on these manifolds the moduli space of classes of positive Sasakian structures has infinitely many components. We also apply our results to give lower bounds on the number of components of the moduli space of Sasaki–Einstein metrics on certain homotopy spheres. Finally, a new family of Sasaki–Einstein metrics of real dimension 20 on S5 is exhibited.

Keywords: Brieskorn manifolds; equivariant symplectic homology; positive Sasakian structure; mean Euler characteristic; Sasaki–Einstein metric

MSC 2010: 53D40; 53D42; 53C25

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Artikelinformationen


Erhalten: 19.07.2015

Revidiert: 10.10.2015

Online erschienen: 20.11.2015

Erschienen im Druck: 01.09.2016


Funding Source: Simons Foundation

Award identifier / Grant number: 245002

The first author was partially supported by a grant (#245002) from the Simons Foundation. The second author was partially supported by CNPq, Brazil. The third author was supported by a stipend from the Humboldt Foundation.


Quellenangabe: Forum Mathematicum, Band 28, Heft 5, Seiten 943–965, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0142.

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