# On stellated spheres and a tightness criterion for combinatorial manifolds

@article{Bagchi2014OnSS,
title={On stellated spheres and a tightness criterion for combinatorial manifolds},
journal={Eur. J. Comb.},
year={2014},
volume={36},
pages={294-313}
}
• Published 24 July 2012
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## References

SHOWING 1-10 OF 42 REFERENCES
FACE ENUMERATION - FROM SPHERES TO MANIFOLDS
We prove a number of new restrictions on the enumerative properties of homology manifolds and semi-Eulerian complexes and posets. These include a determination of the affine span of the fine h-vector
The lower bound conjecture for 3- and 4-manifolds
For any closed connected d-manifold M let ](M) denote the set of vectors / (K)= (]0(K) ..... fd(K)), where K ranges over all triangulations of M and ]k(K) denotes the number of k-simplices of K. The
An infinite family of tight triangulations of manifolds
• Mathematics
J. Comb. Theory, Ser. A
• 2013
Minimal triangulations of sphere bundles over the circle
• Mathematics
J. Comb. Theory, Ser. A
• 2008
On stellated spheres, shellable balls, lower bounds and a combinatorial criterion for tightness
• Mathematics
• 2011
We introduce the $k$-stellated spheres and compare and contrast them with $k$-stacked spheres. It is shown that for $d \geq 2k$, any $k$-stellated sphere of dimension $d$ bounds a unique and
Rigidity and the lower bound theorem 1
SummaryFor an arbitrary triangulated (d-1)-manifold without boundaryC withf0 vertices andf1 edges, define \gamma (C) = f_1 - df_0 + \left( {\begin{array}{*{20}c} {d + 1} \\ 2 \\ \end{array} }
The 9-vertex complex projective plane
• Mathematics
• 1983
In the early days of topology, most of the objects of interest were defined in terms of triangulations, describing a topological space as a union of finitely many vertices, edges, triangles, and