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Topology of moment-angle manifolds arising from flag nestohedra

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Abstract

The author constructs a family of manifolds, one for each n ≥ 2, having a nontrivial Massey n-product in their cohomology for any given n. These manifolds turn out to be smooth closed 2-connected manifolds with a compact torus Tm-action called moment-angle manifolds Z P , whose orbit spaces are simple n-dimensional polytopes P obtained from an n-cube by a sequence of truncations of faces of codimension 2 only (2-truncated cubes). Moreover, the polytopes P are flag nestohedra but not graph-associahedra. The author also describes the numbers β−i,2(i+1)(Q) for an associahedron Q in terms of its graph structure and relates it to the structure of the loop homology (Pontryagin algebra) H*(ΩZ Q ), and then studies higher Massey products in H*(Z Q ) for a graph-associahedron Q.

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Acknowledgments

The author is grateful to Victor Buchstaber and Taras Panov for many helpful discussions and advice, and also thanks James Stasheff and the referee of this article for their valuable comments and suggestions on improving the text.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Ivan Limonchenko

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  1. Ivan Limonchenko
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Correspondence to Ivan Limonchenko.

Additional information

The work was supported by the General Financial Grant from the China Postdoctoral Science Foundation (No. 2016M601486).

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Limonchenko, I. Topology of moment-angle manifolds arising from flag nestohedra. Chin. Ann. Math. Ser. B 38, 1287–1302 (2017). https://doi.org/10.1007/s11401-017-1037-1

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  • DOI: https://doi.org/10.1007/s11401-017-1037-1

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