Description
Abstract: This talk is based on the joint paper arXiv:2006.12182 with David Favero. We will explain how to construct GLSM invariants for a general choice of stability in both the narrow and broad sector cases so that GLSM invariants form a Cohomological Field Theory. This construction is obtained by forming the analogue of a virtual fundamental class which lives in the local cohomology of the twisted Hodge complex. This general construction comes from the use of two new ingredients. First, the use of the Thom-Sullivan and Godement resolutions applied to matrix factorizations are introduced to handle poorly behaved (non-separated) moduli spaces. Second, a localized Chern character map built from the Atiyah class of a matrix factorization is utilized to forgo the use of Hochschild homology.
