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BUCHSBAUM* COMPLEXES CHRISTOS A. ATHANASIADIS AND VOLKMAR WELKER
 

Summary: BUCHSBAUM* COMPLEXES
CHRISTOS A. ATHANASIADIS AND VOLKMAR WELKER
Abstract. A class of finite simplicial complexes, which we call Buchsbaum* over a field,
is introduced. Buchsbaum* complexes generalize triangulations of orientable homology
manifolds as well as doubly Cohen-Macaulay complexes. By definition, the Buchsbaum*
property depends only on the geometric realization and the field. Characterizations in
terms of simplicial homology are given. It is proved that Buchsbaum* complexes are
doubly Buchsbaum. Various constructions, among them one which generalizes convex ear
decompositions, are shown to yield Buchsbaum* simplicial complexes. Graph theoretic
and enumerative properties of Buchsbaum* complexes are investigated.
1. Introduction
A major theme in the study of finite simplicial complexes in the past few decades has
been the interplay between their algebraic, combinatorial, homological and topological
properties. Several classes of simplicial complexes, such as Buchsbaum, Cohen-Macaulay
or Gorenstein complexes, have been introduced and studied in order to isolate important
features of triangulations of fundamental geometric objects, such as balls, spheres and
various other manifolds. We refer the reader to [22] for a comprehensive introduction to
the subject. The objective of this paper is to introduce and develop the basic properties
of a new class of simplicial complexes, named Buchsbaum* complexes, which generalize
triangulations of orientable homology manifolds.

  

Source: Athanasiadis, Christos - Department of Mathematics, University of Athens

 

Collections: Mathematics