On the generalized lower bound conjecture for polytopes and spheres

Satoshi Murai; Eran Nevo

doi:10.1007/s11511-013-0093-y

On the generalized lower bound conjecture for polytopes and spheres

Satoshi Murai, Eran Nevo^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

In 1971, McMullen and Walkup posed the following conjecture, which is called the generalized lower bound conjecture: If P is a simplicial d-polytope then its h-vector (h₀, h₁, ..., h_d) satisfies, Moreover, if h_r-1 = h_r for some, then P can be triangulated without introducing simplices of dimension ≤d - r. The first part of the conjecture was solved by Stanley in 1980 using the hard Lefschetz theorem for projective toric varieties. In this paper, we give a proof of the remaining part of the conjecture. In addition, we generalize this result to a certain class of simplicial spheres, namely those admitting the weak Lefschetz property.

Original language	English
Pages (from-to)	185-202
Number of pages	18
Journal	Acta Mathematica
Volume	210
Issue number	1
DOIs	https://doi.org/10.1007/s11511-013-0093-y
State	Published - 2013
Externally published	Yes

Bibliographical note

Funding Information:
Research of the first author was partially supported by KAKENHI 22740018. Research of the second author was partially supported by Marie Curie grant IRG-270923 and by an ISF grant.

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On the generalized lower bound conjecture for polytopes and spheres

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