Equivariant infinite loop space theory, I. The space level story

We rework and generalize equivariant infinite loop space theory, which shows how to construct G-spectra from G-spaces with suitable structure. There is a naive version which gives naive G-spectra for any topological group G, but our focus is on the construction of genuine G-spectra when G is finite. We give new information about the Segal and operadic equivariant infinite loop space machines, supplying many details that are missing from the literature, and we prove by direct comparison that the two machines give equivalent output when fed equivalent input. The proof of the corresponding nonequivariant uniqueness theorem, due to May and Thomason, works for naive G-spectra for general G but fails hopelessly for genuine G-spectra when G is finite. Even in the nonequivariant case, our comparison theorem is considerably more precise, giving a direct point-set level comparison. We have taken the opportunity to update this general area, equivariant and nonequivariant, giving many new proofs, filling in some gaps, and giving some corrections to results in the literature.Comment: 94 page

The equivariant parametrized hh-cobordism theorem, the non-manifold part

We construct a map from the suspension $G$-spectrum $\Sigma_G^\infty M$ of a smooth compact $G$-manifold to the equivariant $A$-theory spectrum $A_G(M)$, and we show that its fiber is, on fixed points, a wedge of stable $h$-cobordism spectra. This map is constructed as a map of spectral Mackey functors, which is compatible with tom Dieck style splitting formulas on fixed points. In order to synthesize different definitions of the suspension $G$-spectrum as a spectral Mackey functor, we present a new perspective on spectral Mackey functors, viewing them as multifunctors on indexing categories for "rings on many objects" and modules over such. This perspective should be of independent interest

Equivariant AA-theory

We give a new construction of the equivariant $K$-theory of group actions [\textit{C. Barwick}, "Spectral Mackey functors and equivariant algebraic -theory (I)", Adv. Math. 304, 646-727 (2017; Zbl 1348.18020) and \textit{C. Barwick} et al., "Spectral Mackey functors and equivariant algebraic -theory (II)", Preprint (2015); \url{arXiv:1505.03098}], producing an infinite loop $G$-space for each Waldhausen category with $G$-action, for a finite group $G$. On the category $R(X)$ of retractive spaces over a $G$-space $X$, this produces an equivariant lift of Waldhausen's functor $A(X)$, and we show that the $H$-fixed points are the bivariant $A$-theory of the fibration $X_{hH}\to BH$. We then use the framework of spectral Mackey functors to produce a second equivariant refinement $A_G(X)$ whose fixed points have tom Dieck type splittings. We expect this second definition to be suitable for an equivariant generalization of the parametrized $h$-cobordism theorem. <br

Equivariant AA-theory

We give a new construction of the equivariant $K$-theory of group actions [\textit{C. Barwick}, "Spectral Mackey functors and equivariant algebraic -theory (I)", Adv. Math. 304, 646-727 (2017; Zbl 1348.18020) and \textit{C. Barwick} et al., "Spectral Mackey functors and equivariant algebraic -theory (II)", Preprint (2015); \url{arXiv:1505.03098}], producing an infinite loop $G$-space for each Waldhausen category with $G$-action, for a finite group $G$. On the category $R(X)$ of retractive spaces over a $G$-space $X$, this produces an equivariant lift of Waldhausen's functor $A(X)$, and we show that the $H$-fixed points are the bivariant $A$-theory of the fibration $X_{hH}\to BH$. We then use the framework of spectral Mackey functors to produce a second equivariant refinement $A_G(X)$ whose fixed points have tom Dieck type splittings. We expect this second definition to be suitable for an equivariant generalization of the parametrized $h$-cobordism theorem

Cut and paste invariants of manifolds via algebraic K-theory

Recent work of Jonathan Campbell and Inna Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic $K$-theory, and applying these tools to studying the Grothendieck ring of varieties. In this paper we give a new application of their framework: we construct a $K$-space that recovers the classical $\mathrm{SK}$ ("schneiden und kleben," German for "cut and paste") groups for manifolds on $\pi_0$, and we construct a derived version of the Euler characteristic

Lentiviral gene therapy rescues p47phox chronic granulomatous disease and the ability to fight Salmonella infection in mice

Chronic granulomatous disease (CGD) is an inherited primary immunodeficiency disorder characterised by recurrent and often life-threatening infections and hyperinflammation. It is caused by defects of the phagocytic NADPH oxidase, a multicomponent enzyme system responsible for effective pathogen killing. A phase I/II clinical trial of lentiviral gene therapy is underway for the most common form of CGD, X-linked, caused by mutations in the gp91phox subunit of the NADPH oxidase. We propose to use a similar strategy to tackle p47phox-deficient CGD, caused by mutations in NCF1, which encodes the p47phox cytosolic component of the enzymatic complex. We generated a pCCLCHIM-p47phox lentiviral vector, containing the chimeric Cathepsin G/FES myeloid promoter and a codon-optimised version of the human NCF1 cDNA. Here we show that transduction with the pCCLCHIM-p47phox vector efficiently restores p47phox expression and biochemical NADPH oxidase function in p47phox-deficient human and murine cells. We also tested the ability of our gene therapy approach to control infection by challenging p47phox-null mice with Salmonella Typhimurium, a leading cause of sepsis in CGD patients, and found that mice reconstituted with lentivirus-transduced hematopoietic stem cells had a reduced bacterial load compared with untreated mice. Overall, our results potentially support the clinical development of a gene therapy approach using the pCCLCHIM-p47phox vector

Overview of Plasma Lens Experiments and Recent Results at SPARC_LAB

Beam injection and extraction from a plasma module is still one of the crucial aspects to solve in order to produce high quality electron beams with a plasma accelerator. Proper matching conditions require to focus the incoming high brightness beam down to few microns size and to capture a high divergent beam at the exit without loss of beam quality. Plasma-based lenses have proven to provide focusing gradients of the order of kT/m with radially symmetric focusing thus promising compact and affordable alternative to permanent magnets in the design of transport lines. In this paper an overview of recent experiments and future perspectives of plasma lenses is reported

NF-κB Hyper-Activation by HTLV-1 Tax Induces Cellular Senescence, but Can Be Alleviated by the Viral Anti-Sense Protein HBZ

Activation of I-κB kinases (IKKs) and NF-κB by the human T lymphotropic virus type 1 (HTLV-1) trans-activator/oncoprotein, Tax, is thought to promote cell proliferation and transformation. Paradoxically, expression of Tax in most cells leads to drastic up-regulation of cyclin-dependent kinase inhibitors, p21CIP1/WAF1 and p27KIP1, which cause p53-/pRb-independent cellular senescence. Here we demonstrate that p21CIP1/WAF1-/p27KIP1-mediated senescence constitutes a checkpoint against IKK/NF-κB hyper-activation. Senescence induced by Tax in HeLa cells is attenuated by mutations in Tax that reduce IKK/NF-κB activation and prevented by blocking NF-κB using a degradation-resistant mutant of I-κBα despite constitutive IKK activation. Small hairpin RNA-mediated knockdown indicates that RelA induces this senescence program by acting upstream of the anaphase promoting complex and RelB to stabilize p27KIP1 protein and p21CIP1/WAF1 mRNA respectively. Finally, we show that down-regulation of NF-κB by the HTLV-1 anti-sense protein, HBZ, delay or prevent the onset of Tax-induced senescence. We propose that the balance between Tax and HBZ expression determines the outcome of HTLV-1 infection. Robust HTLV-1 replication and elevated Tax expression drive IKK/NF-κB hyper-activation and trigger senescence. HBZ, however, modulates Tax-mediated viral replication and NF-κB activation, thus allowing HTLV-1-infected cells to proliferate, persist, and evolve. Finally, inactivation of the senescence checkpoint can facilitate persistent NF-κB activation and leukemogenesis