ﻻ يوجد ملخص باللغة العربية
We resolve a conjecture of Kalai asserting that the $g_2$-number of any simplicial complex $Delta$ that represents a connected normal pseudomanifold of dimension $dgeq 3$ is at least as large as ${d+2 choose 2}m(Delta)$, where $m(Delta)$ denotes the minimum number of generators of the fundamental group of $Delta$. Furthermore, we prove that a weaker bound, $h_2(Delta)geq {d+1 choose 2}m(Delta)$, applies to any $d$-dimensional pure simplicial poset $Delta$ all of whose faces of co-dimension $geq 2$ have connected links. This generalizes a result of Klee. Finally, for a pure relative simplicial poset $Psi$ all of whose vertex links satisfy Serres condition $(S_r)$, we establish lower bounds on $h_1(Psi),ldots,h_r(Psi)$ in terms of the $mu$-numbers introduced by Bagchi and Datta.
We study face numbers of simplicial complexes that triangulate manifolds (or even normal pseudomanifolds) with boundary. Specifically, we establish a sharp lower bound on the number of interior edges of a simplicial normal pseudomanifold with boundar
We show that J_n, the Stanley-Reisner ideal of the n-cycle, has a free resolution supported on the (n-3)-dimensional simplicial associahedron A_n. This resolution is not minimal for n > 5; in this case the Betti numbers of J_n are strictly smaller th
This paper has two related parts. The first generalizes Hochsters formula on resolutions of Stanley-Reisner rings to a colorful version, applicable to any proper vertex-coloring of a simplicial complex. The second part examines a universal system of
In this paper, we attempt to develop the Quillen Suslin theory for the algebraic fundamental group of a ring. We give a surjective group homomorphism from the algebraic fundamental group of the field of the real numbers to the group of integers. At t
We define the principal divisor of a free noncommuatative function. We use these divisors to compare the determinantal singularity sets of free noncommutative functions. We show that the divisor of a noncommutative rational function is the difference