Course Title: The Homotopy Theory of Polyhedral Products

Instructors: A. Bahri, T. Panov and S. Theriault.

* Please note this course will be going online starting Wednesday April 29th at 10:30am-12:00pm *

Join Zoom Meeting
https://zoom.us/j/8264969360
Meeting ID: 826 496 9360

The course will be a comprehensive introduction to the homotopy theory of polyhedral products covering topics from the list below:

TOPICS:

1. Introduction (AB)

2. Motivation (AB)

3. The origin of polyhedral products in toric topology (TP)

4. The introduction of moment-angle manifolds (TP)

5. Moment-angle manifolds as intersections of quadrics (TBA)

6. The cohomology of moment-angle complexes. (TP)

7. Other structures on moment-angle manifolds (TP)

8. The exponentiation property of polyhedral products. (AB)

9. Fibrations (TBA)

10. Stable and unstable decompositions of polybedral products. (AB)

11. Equivariance of the stable splitting and applications. (AB)

12. The case A_i = a point, (Part I) (AB)

13. The cohomology of polyhedral products: spectral sequence (AB)

14. The cohomology of polyhedral products: geometric approach (AB)

15. The case A_i = a point, (Part II) (ST)

16. Polyhedral products and the Golodness property of monomial ideal rings (ST)

17. Higher Whitehead products and loops spaces (ST)

LITERATURE:

1. A. Bahri, M.Bendersky, F. R. Cohen,  Polyhedral products and features of their homotopy theory,
to appear in  Handbook of Homotopy Theory, Haynes Miller, editor.
https://arxiv.org/pdf/1903.04114.pdf

2. V. Buchstaber and T. Panov. Toric Topology, Mathematical Surveys and Monographs, vol. 204, AMS, Providence, RI, 2015.