Algebras over equivariant sphere spectra

AbstractWe study the category of algebras over the sphere G-spectrum of a compact Lie group G. A priori, this category depends on which representations appear in the underlying universe on which G-spectra are indexed, but we prove that different universes give rise to equivalent categories of point-set level algebras. The relevant change of universe functors are defined on categories of modules over sphere spectra and induce the classical change of universe functors (which are not equivalences!) on passage to stable homotopy categories. In particular, we show how to construct equivariant algebras from nonequivariant algebras by change of universe. This gives a reservoir of equivariant examples to which recently developed algebraic techniques in stable homotopy theory can be applied

Rings, modules, and algebras in infinite loop space theory

We give a new construction of the algebraic $K$-theory of small permutative categories that preserves multiplicative structure, and therefore allows us to give a unified treatment of rings, modules, and algebras in both the input and output. This requires us to define multiplicative structure on the category of small permutative categories. The framework we use is the concept of multicategory, a generalization of symmetric monoidal category that precisely captures the multiplicative structure we have present at all stages of the construction. Our method ends up in Smith's category of symmetric spectra, with an intermediate stop at a new category that may be of interest in its own right, whose objects we call symmetric functors.Comment: 59 pages, 1 figur

Twisted equivariant K-theory, groupoids and proper actions

In this paper we define twisted equivariant K-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite CW-complexes with equivariant stable projective bundles. A classification of these bundles is shown. We also obtain a completion theorem and apply these results to proper actions of groups.Comment: 26 page

A model structure for coloured operads in symmetric spectra

We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This allows us to treat R-module spectra (where R is a cofibrant ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as its first term. Using this model structure, we give suficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures.Comment: 16 page

Warming shortens flowering seasons of tundra plant communities

Advancing phenology is one of the most visible effects of climate change on plant communities, and has been especially pronounced in temperature-limited tundra ecosystems. However, phenological responses have been shown to differ greatly between species, with some species shifting phenology more than others. We analysed a database of 42,689 tundra plant phenological observations to show that warmer temperatures are leading to a contraction of community-level flowering seasons in tundra ecosystems due to a greater advancement in the flowering times of late-flowering species than early-flowering species. Shorter flowering seasons with a changing climate have the potential to alter trophic interactions in tundra ecosystems. Interestingly, these findings differ from those of warmer ecosystems, where early-flowering species have been found to be more sensitive to temperature change, suggesting that community-level phenological responses to warming can vary greatly between biomes