FACE ENUMERATION - FROM SPHERES TO MANIFOLDS
By Ed Swartz. 2007
68 citations recorded by the source corpus.
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 of balanced semi-Eulerian complexes and the toric h-vector of semi-Eulerian posets. The lower bounds on simplicial homology manifolds, when combined with higher dimensional analogues of Walkup�s 3-dimensional constructions [47], allow us to give a complete characterization of the f-vectors of arbitrary simplicial triangulations of S1 × S3 , CP2, K3 surfaces, and (S2 × S2) # (S2 × S2). We also establish a principle which leads to a conjecture for homology manifolds which is almost logically equivalent to the g-conjecture for homology spheres. Lastly, we show that with sufficiently many vertices, every triangulable homology manifold without boundary of dimension three or greater can be triangulated in a 2-neighborly fashion.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/82371f2f059a01f72f90dd0cdca722024b077b59
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Gorenstein rings through face rings of manifolds (2008, methodology): “ is used to explore the relationship between the gconjecture and Kalai’s conjecture. Section 4 is devoted to the proof of Theorem 1.5. The proofs of Theorems 1.4 and 1.5 rely heavily on a result from [16] relating k(lkv) (for a vertex v of ∆) to the principal ideal (xv) ⊂ k(∆). 2 Socles of homology ”