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- W2962702377 abstract "Let $X$ be a $2n$-manifold with a locally standard action of a compact torus $T^n$. If the free part of action is trivial and proper faces of the orbit space $Q$ are acyclic, then there are three types of homology classes in $X$: (1) classes of face submanifolds; (2) $k$-dimensional classes of $Q$ swept by actions of subtori of dimensions $<k$; (3) relative $k$-classes of $Q$ modulo $partial Q$ swept by actions of subtori of dimensions $geqslant k$. The submodule of $H_*(X)$ spanned by face classes is an ideal in $H_*(X)$ with respect to the intersection product. It is isomorphic to $(mathbb{Z}[S_Q]/Theta)/W$, where $mathbb{Z}[S_Q]$ is the face ring of the Buchsbaum simplicial poset $S_Q$ dual to $Q$; $Theta$ is the linear system of parameters determined by the characteristic function; and $W$ is a certain submodule, lying in the socle of $mathbb{Z}[S_Q]/Theta$. Intersections of homology classes different from face submanifolds are described in terms of intersections on $Q$ and $T^n$." @default.
- W2962702377 created "2019-07-30" @default.
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- W2962702377 date "2016-01-01" @default.
- W2962702377 modified "2023-09-28" @default.
- W2962702377 title "Homology cycles in manifolds with locally standard torus actions" @default.
- W2962702377 doi "https://doi.org/10.4310/hha.2016.v18.n1.a1" @default.
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