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| Topology of Moment-Angle Manifolds Arising fromFlag Nestohedra |
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Citation： |
Ivan LIMONCHENKO.Topology of Moment-Angle Manifolds Arising fromFlag Nestohedra[J].Chinese Annals of Mathematics B,2017,38(6):1287~1302 |
| Page view： 1273
Net amount： 1687 |
Authors： |
Ivan LIMONCHENKO; |
Foundation： |
The work was supported by the General Financial Grant
from the China Postdoctoral Science Foundation (No.2016M601486). |
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| Abstract： |
The author constructs a family of manifolds, one for each $n\geq 2$,
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 $\mathbb T^m$-action called
moment-angle manifolds $\mathcal Z_P$, 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
$\beta^{-i,2(i+1)}(Q)$ for an associahedron $Q$ in terms of its
graph structure and relates it to the structure of the loop homology
(Pontryagin algebra) $H_{*}(\Omega\mathcal Z_Q)$, and then studies
higher Massey products in $H^{*}(\mathcal Z_Q)$ for a
graph-associahedron $Q$. |
Keywords： |
Moment-angle manifold, Flag nestohedra, Stanley-Reisner ring, Massey products, Graph-associahedron |
Classification： |
13F55, 55S30, 52B11 |
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