TY - JOUR
T1 - A generalized lower bound theorem for balanced manifolds
AU - Juhnke-Kubitzke, Martina
AU - Murai, Satoshi
AU - Novik, Isabella
AU - Sawaske, Connor
N1 - Funding Information:
Juhnke-Kubitzke’s research is partially supported by German Research Council DFG-GRK 1916. Murai’s research is partially supported by JSPS KAKENHI JP16K05102. Novik’s research is partially supported by NSF grant DMS-1361423.
Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - A simplicial complex of dimension d- 1 is said to be balanced if its graph is d-colorable. Juhnke-Kubitzke and Murai proved an analogue of the generalized lower bound theorem for balanced simplicial polytopes. We establish a generalization of their result to balanced triangulations of closed homology manifolds and balanced triangulations of orientable homology manifolds with boundary under an additional assumption that all proper links of these triangulations have the weak Lefschetz property. As a corollary, we show that if Δ is an arbitrary balanced triangulation of any closed homology manifold of dimension d- 1 ≥ 3 , then 2h2(Δ)-(d-1)h1(Δ)≥4(d2)(β~1(Δ)-β~0(Δ)), thus verifying a conjecture by Klee and Novik. To prove these results we develop the theory of flag h′ ′-vectors.
AB - A simplicial complex of dimension d- 1 is said to be balanced if its graph is d-colorable. Juhnke-Kubitzke and Murai proved an analogue of the generalized lower bound theorem for balanced simplicial polytopes. We establish a generalization of their result to balanced triangulations of closed homology manifolds and balanced triangulations of orientable homology manifolds with boundary under an additional assumption that all proper links of these triangulations have the weak Lefschetz property. As a corollary, we show that if Δ is an arbitrary balanced triangulation of any closed homology manifold of dimension d- 1 ≥ 3 , then 2h2(Δ)-(d-1)h1(Δ)≥4(d2)(β~1(Δ)-β~0(Δ)), thus verifying a conjecture by Klee and Novik. To prove these results we develop the theory of flag h′ ′-vectors.
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U2 - 10.1007/s00209-017-1981-1
DO - 10.1007/s00209-017-1981-1
M3 - Article
AN - SCOPUS:85034092962
VL - 289
SP - 921
EP - 942
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3-4
ER -