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- W2473222805 abstract "We study the classes of simplicial and cubical complexes. The common theme in studying these two classes of complexes is to discover lower bounds on their face numbers as a function of their underlying geometric structures. In the first part, we study the family of balanced simplicial complexes. We begin by bounding the number of faces in a balanced pseudomanifold in terms of the size of a minimal generating set of its fundamental group. We go on to study other classes of balanced simplicial complexes, namely the classes of doubly Cohen-Macaulay and Buchsbaum* complexes, which include balanced triangulations of spheres and orientable manifolds, respectively. We prove an analogue of the Barnette's Lower Bound Theorem (LBT) for these complexes by constructing a family of balanced spheres that simultaneously minimize all face numbers as a function of the dimension of the complex and its number of vertices. In the second part; we study the family of cubical pseudomanifolds. We begin by proving that the boundary complex of a d-dimensional cube has the minimal face numbers among all (d – 1)-dimensional cubical pseudomanifolds. We go on to study the class of cubical polytopes more generally, proving some special cases of the LBT for cubical complexes. We conclude by proving a version of the Dehn-Sommerville equations for cubical manifolds with boundary." @default.
- W2473222805 created "2016-07-22" @default.
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- W2473222805 date "2010-01-01" @default.
- W2473222805 modified "2023-09-26" @default.
- W2473222805 title "Lower bound theorems for simplicial and cubical complexes" @default.
- W2473222805 hasPublicationYear "2010" @default.
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