G-symmetric spectra, semistability and the multiplicative norm

In this paper we develop the basic homotopy theory of G-symmetric spectra (that is, symmetric spectra with a G-action) for a finite group G, as a model for equivariant stable homotopy with respect to a G-set universe. This model lies in between Mandell's equivariant symmetric spectra and the G-orthogonal spectra of Mandell and May and is Quillen equivalent to the two. We further discuss equivariant semistability, construct model structures on module, algebra and commutative algebra categories and describe the homotopical properties of the multiplicative norm in this context.Comment: Final published versio

Symmetric products and subgroup lattices

Let G be a finite group. We show that the rational homotopy groups of symmetric products of the G-equivariant sphere spectrum are naturally isomorphic to the rational homology groups of certain subcomplexes of the subgroup lattice of G.Comment: final published versio

Commuting matrices and Atiyah's Real K-theory

We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting n-tuples in the stable orthogonal group, as well as of the coefficient ring for commutative orthogonal K-theory.Comment: Minor changes. To appear in Journal of Topolog

Symmetric products, subgroup lattices and filtrations of global K-theory

This thesis consists of two projects in equivariant stable homotopy theory. In the first we study the rational homotopy groups of symmetric products of the G-sphere spectrum and show that they are naturally isomorphic to the rational homology groups of certain subcomplexes of the subgroup lattice of G. In the second we investigate global equivariant versions of spectrum level filtrations introduced by Arone and Lesh which interpolate between topological/algebraic K-theory and the Eilenberg-MacLane spectrum for the integers. We determine the global homotopy type of the subquotients and use this description to obtain algebraic formulas for filtrations of representation rings that arise on 0-th homotopy groups

The Neuromodulatory Effects of Sex Hormones on Functional Cerebral Asymmetries and Cognitive Control

Nearly 20 years ago, Hausmann and Güntürkün (2000a, 2000b) published a review article in the Journal of Neuropsychology/Zeitschrift für Neuropsychologie on the influences of sex hormones on functional cerebral asymmetries (FCAs). They further presented a neuroendocrinological model (Hausmann & Güntürkün, 2000c) that could potentially explain how sex hormones modulate FCAs. Their model proposed that high levels of progesterone reduce the synaptic efficiency of cortico-cortical transmission, leading to a reduction of FCAs. However, empirical data testing their hypothesis directly were missing. Using various approaches, we have now gathered behavioral, electrophysiological, and neuroimaging data that partly support the original idea, while also pointing toward estradiol-modulating FCAs. The current review provides an update on this fascinating topic and briefly explores clinical applications

Invariant prime ideals in equivariant Lazard rings

Let $A$ be an abelian compact Lie group. In this paper we compute the spectrum of invariant prime ideals of the $A$-equivariant Lazard ring, or equivalently the spectrum of points of the moduli stack of $A$-equivariant formal groups. We further show that this spectrum is homeomorphic to the Balmer spectrum of compact $A$-spectra, with the comparison map induced by equivariant complex bordism homology.Comment: 43 pages, comments welcom

Proper Equivariant Stable Homotopy Theory

All five authors were supported by the Hausdorff Center for Mathematics at the University of Bonn (DFG GZ 2047/1, project ID 390685813) and by the Centre for Symmetry and Deformation at the University of Copenhagen (CPH-SYM-DNRF92); we would like to thank these two institutions for their hospitality, support and the stimulating atmosphere. Hausmann, Patchkoria and Schwede were partially supported by the DFG Priority Programme 1786 ‘Homotopy Theory and Algebraic Geometry’. Work on this monograph was funded by the ERC Advanced Grant ‘KL2MG-interactions’ of L¨uck (Grant ID 662400), granted by the European Research Council. Patchkoria was supported by the Shota Rustaveli National Science Foundation Grant 217-614. Patchkoria and Schwede would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme ‘Homotopy harnessing higher structures’, when work on this paper was undertaken (EPSRC grant number EP/R014604/1). We would also like to thank Bob Oliver and Søren Galatius for helpful conversations on topics related to this project, and the anonymous referee for his or her careful reading and the many useful comments.Peer reviewedPostprin