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- W4313303738 abstract "Inertia orbifolds homotopy-quotiented by rotation of geometric loops play a fundamental role not only in ordinary cyclic cohomology, but more recently in constructions of equivariant Tate-elliptic cohomology and generally of transchromatic characters on generalized cohomology theories. Nevertheless, existing discussion of such cyclified stacks has been relying on ad-hoc component presentations with intransparent and unverified stacky homotopy type. Following our previous formulation of transgression of cohomological charges (double dimensional reduction), we explain how cyclification of infinity-stacks is a fundamental and elementary base-change construction over moduli stacks in cohesive higher topos theory (cohesive homotopy type theory). We prove that Ganter/Huan's extended inertia groupoid used to define equivariant quasi-elliptic cohomology is indeed a model for this intrinsically defined cyclification of orbifolds, and we show that cyclification implements transgression in group cohomology in general, and hence in particular the transgression of degree-4 twists of equivariant Tate-elliptic cohomology to degree-3 twists of orbifold K-theory on the cyclified orbifold. As an application, we show that the universal shifted integral 4-class of equivariant 4-Cohomotopy theory on ADE-orbifolds induces the Platonic 4-twist of ADE-equivariant Tate-elliptic cohomology; and we close by explaining how this should relate to elliptic M5-brane genera, under our previously formulated Hypothesis H." @default.
- W4313303738 created "2023-01-06" @default.
- W4313303738 creator A5035762576 @default.
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- W4313303738 date "2022-12-28" @default.
- W4313303738 modified "2023-09-23" @default.
- W4313303738 title "Cyclification of Orbifolds" @default.
- W4313303738 doi "https://doi.org/10.48550/arxiv.2212.13836" @default.
- W4313303738 hasPublicationYear "2022" @default.
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