Cw Posets after the Poincare Conjecture
نویسنده
چکیده
Anders Björner characterized which finite graded partially ordered sets arise as the closure relation on cells of a finite regular CW complex. His characterization of these “CW posets” required each open interval (0̂, u) to have order complex homeomorphic to a sphere of dimension rk(u)− 2. Work of Danaraj and Klee showed that sufficient conditions were for the poset to be thin and shellable. The proof of the Poincare Conjecture enables the requirement of shellability to be replaced by the homotopy CohenMacaulay property. This expands the range of tools that may be used to prove a poset is a CW poset.
منابع مشابه
Regular Cell Complexes in Total Positivity
Fomin and Shapiro conjectured that the link of the identity in the Bruhat stratification of the totally nonnegative real part of the unipotent radical of a Borel subgroup in a semisimple, simply connected algebraic group defined and split over R is a regular CW complex homeomorphic to a ball. The main result of this paper is a proof of this conjecture. This completes the solution of the questio...
متن کاملPolyhedral Representation of Discrete Morse Functions on Regular Cw Complexes and Posets Preliminary Draft
It is proved that the critical cells of a discrete Morse function in the sense of Forman on a finite regular CW complex can always be detected by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the complex. The proof is stated in terms of discrete Morse functions on a class of posets that is slightly broader t...
متن کاملOrthogonal Polynomials Represented by CW-Spheres
Given a sequence {Qn(x)}∞n=0 of symmetric orthogonal polynomials, defined by a recurrence formula Qn(x) = νn · x · Qn−1(x) − (νn − 1) · Qn−2(x) with integer νi’s satisfying νi ≥ 2, we construct a sequence of nested Eulerian posets whose ceindex is a non-commutative generalization of these polynomials. Using spherical shellings and direct calculations of the cd-coefficients of the associated Eul...
متن کاملNested chain partitions of LYM posets
A long-standing conjecture states that all LYM posets possess nested chain partitions. We verify this conjecture for posets of rank 2. © 2004 Elsevier B.V. All rights reserved.
متن کاملPossible Solution to the Poincare Conjecture
The Poincare conjecture is analyzed in the context of Calabi-Yau n-folds. A simple treatment is given by embedding the three-manifolds into these CY manifolds, and then taking the orbifold limit. The higher-dimensional proofs are also available in this context.
متن کامل