On the cohomology rings of quotients of moment-angle complexes: naturality

On the cohomology rings of quotients of moment-angle complexes: naturality

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Xin Fu, Ajou University

*Please note the time change* 10:00AM EDT

Zoom link: https://princeton.zoom.us/j/92116764865

Passcode: 114700

A moment-angle complex Z comes with the natural action of a torus T.  Let K be a closed subgroup of T. The quotient Z/is a topological analogue of toric varieties with Z corresponding to the Cox construction.  A recent work of Franz has determined the cohomology rings of Z/K by free K-actions. In this talk, we discuss the naturality of Franz’s ring isomorphisms with respect to toric morphisms. In general, there are twisting terms, which we will describe explicitly. Then we will see examples showing trivial and nontrivial twisting terms, which can explain the multiplicative results related to the cohomology of such spaces.

This is a joint work with Matthias Franz.