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- W4285786518 abstract "We extend several $g$-type theorems for connected, orientable homology manifolds without boundary to manifolds with boundary. As applications of these results we obtain Kuhnel-type bounds on the Betti numbers as well as on certain weighted sums of Betti numbers of manifolds with boundary. Our main tool is the completion $hatDelta$ of a manifold with boundary $Delta$; it is obtained from $Delta$ by coning off the boundary of $Delta$ with a single new vertex. We show that despite the fact that $hat{Delta}$ has a singular vertex, its Stanley--Reisner ring shares a few properties with the Stanley--Reisner rings of homology spheres. We close with a discussion of a connection between three lower bound theorems for manifolds, PL-handle decompositions, and surgery." @default.
- W4285786518 created "2022-07-19" @default.
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- W4285786518 date "2019-09-15" @default.
- W4285786518 modified "2023-10-16" @default.
- W4285786518 title "$g$-vectors of manifolds with boundary" @default.
- W4285786518 doi "https://doi.org/10.48550/arxiv.1909.06729" @default.
- W4285786518 hasPublicationYear "2019" @default.
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