Properness for scaled gauged maps

Properness for Scaled Gauged Maps

We prove properness of moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet [42] and Schmitt [48]. The proof combines a git construction of Schmitt [48], properness for twisted stable maps by Abramovich-Vistoli [1], a variation of a boundedness argument due to Ciocan-Fontanine-Kim-Maulik [13], and a removal of singularities for bundles on surfaces in Colliot-Thél...

Stable Gauged Maps

We give an introduction to moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet [55] and Schmitt [61], and the associated integrals giving rise to gauged Gromov-Witten invariants. We survey various applications to cohomological and Ktheoretic Gromov-Witten invariants.

A-properness and Fixed Point Theorems for Dissipative Type Maps

The A-proper class arises naturally when one considers the approximation solvability of nonlinear equations, that is, obtaining solutions of infinite-dimensional problems as limits of solutions of related finite-dimensional problems. The class was first introduced by Petryshyn, who made many important contributions to the theory, see, for example, [17, 18] for a good account of this. The A-prop...

Testing the usability of well scaled mobile maps for consumers

Properness without Elementaricity

We present reasons for developing a theory of forcing notions which satisfy the properness demand for countable models which are not necessarily elementary sub-models of some (H(χ),∈). This leads to forcing notions which are “reasonably” definable. We present two specific properties materializing this intuition: nep (non-elementary properness) and snep (Souslin non-elementary properness) and al...