THE HOMOTOPY TYPE OF THE POLYHEDRAL PRODUCT FOR SHIFTED COMPLEXES

By J. Grbić, S. Theriault. 2011

79 citations recorded by the source corpus.

Abstract We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if K is a shifted simplicial complex on n vertices, X 1 , … , X n are pointed connected C W -complexes and C X i is the cone on  X i , then the polyhedral product determined by K and the pairs ( C X i , X i ) is homotopy equivalent to a wedge of suspensions of smashes of the X i ’s. Earlier work of the authors dealt with the special case where each X i is a loop space. New techniques are introduced to prove the general case. These have the advantage of simplifying the earlier results and of being sufficiently general to show that the conjecture holds for a substantially larger class of simplicial complexes. We discuss connections between polyhedral products and toric topology, combinatorics, and classical homotopy theory.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/13f3ffdb183ad0432ddac8dabea34a3659bcf635

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. S. Gitler
2. A. Bahri
3. Martin Bendersky
4. Frederick R. Cohen
5. T. Panov
6. Jie Wu
7. M. Masuda

In Discrete Mathematics and Combinatorics

1. T. Panov
2. S. Theriault
3. J. Grbić
4. S. Gitler
5. A. Bahri
6. Martin Bendersky
7. Frederick R. Cohen
8. Jie Wu

In Mathematical Physics

1. T. Panov
2. S. Theriault
3. J. Grbić
4. S. Gitler
5. Frederick R. Cohen
6. A. Bahri
7. Martin Bendersky
8. Jie Wu

Citations in the corpus

• Operations on polyhedral products and a new topological construction of infinite families of toric manifolds (2010, methodology): “Applications of the methods and results developed here have appeared in [24, 25, 15, 18, 10, 23], and [19].”
• The homotopy types of moment-angle complexes for flag complexes (2012, background): “Recently, homotopy theoretical generalisations of momentangle complexes and related spaces under the unifying umbrella of polyhedral products (see, for example,[1],[15], [16], [17]) have brought stable and unstable decomposition techniques to bear, and are leading to an improved understanding of tor”