ALGEBRAIC COMBINATORICS

no. 4
g-vectors of manifolds with boundary
Novik, Isabella1; Swartz, Ed2
1 Department of Mathematics University of Washington Seattle, WA 98195-4350, USA
2 Department of Mathematics Cornell University Ithaca, NY 14853-4201, USA
Algebraic Combinatorics, Volume 3 (2020) no. 4, pp. 887-911.

We extend several g-type theorems for connected, orientable homology manifolds without boundary to manifolds with boundary. As applications of these results we obtain Kühnel-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 Δ ^ of a manifold with boundary Δ; it is obtained from Δ by coning off the boundary of Δ with a single new vertex. We show that despite the fact that Δ ^ 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.

Received:
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Accepted:
Published online:
DOI: 10.5802/alco.121
Classification: 05E45, 05E40, 13F55, 52B05, 55U10, 57Q15
Keywords: Homology manifolds with boundary, $g$-numbers, $g$-theorem, Stanley-Reisner rings, local cohomology, socle, Gorenstein rings.
Novik, Isabella 1; Swartz, Ed 2

1 Department of Mathematics University of Washington Seattle, WA 98195-4350, USA
2 Department of Mathematics Cornell University Ithaca, NY 14853-4201, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Novik, Isabella; Swartz, Ed. $g$-vectors of manifolds with boundary. Algebraic Combinatorics, Volume 3 (2020) no. 4, pp. 887-911. doi : 10.5802/alco.121. https://alco.centre-mersenne.org/articles/10.5802/alco.121/

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