g-vectors of manifolds with boundary
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: 2019-09-27
Revised: 2020-03-24
Accepted: 2020-03-27
Published online: 2020-08-20
DOI: https://doi.org/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.
@article{ALCO_2020__3_4_887_0,
     author = {Novik, Isabella and Swartz, Ed},
     title = {$g$-vectors of manifolds with boundary},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {3},
     number = {4},
     year = {2020},
     pages = {887-911},
     doi = {10.5802/alco.121},
     language = {en},
     url = {alco.centre-mersenne.org/item/ALCO_2020__3_4_887_0/}
}
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/item/ALCO_2020__3_4_887_0/

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