Project description

This project proposal is concerned with several basic questions about the foundations of equivariant stable homotopy theory. The main goals are to establish odd primary ridigity results for G-equivariant stable homotopy category for any finite group $G$, and to investigate to what extent the results and methods can be adapted to equivariant homotopy theory for compact Lie groups. Another aim is to develop the theory of equivariant derivators and give a universal characterization of equivariant stable homotopy theory, for finite groups, in terms of derivators.

Related publications

Irakli Patchkoria, Rigidity in Equivariant Stable Homotopy Theory, Algebr. Geom. Topol. 16 (2016), no. 4, 2159–2227.

Irakli Patchkoria, Constanze Roitzheim, Rigidity and exotic models for $v_1$-local $G$-equivariant stable homotopy theory, Math. Z. 295 (2020), no. 1-2, 839--875.

Irakli Patchkoria, On exotic equivalences and a theorem of Franke, Bulletin of the London Mathematical Society 49 (2017), 1085--1099