Chern classes and extraspecial groups

The mod-p cohomology ring of the extraspecial p-group of exponent p is studied for odd p. We investigate the subquotient ch(G) generated by Chern classes modulo the nilradical. The subring of ch(G) generated by Chern classes of one-dimensional representations was studied by Tezuka and Yagita. The subring generated by the Chern classes of the faithful irreducible representations is a polynomial algebra. We study the interplay between these two families of generators, and obtain some relations between them

Rigidification of quasi-categories

We give a new construction for rigidifying a quasi-category into a simplicial category, and prove that it is weakly equivalent to the rigidification given by Lurie. Our construction comes from the use of necklaces, which are simplicial sets obtained by stringing simplices together. As an application of these methods, we use our model to reprove some basic facts from Lurie's "Higher Topos Theory" regarding the rigidification process.Comment: 26 page

On realizing diagrams of Pi-algebras

Given a diagram of Pi-algebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized Pi-algebras. This extends a program begun in [J. Pure Appl. Alg. 103 (1995) 167-188] and [Topology 43 (2004) 857-892] to study the realization of a single Pi-algebra. In particular, we explicitly analyze the simple case of a single map, and provide a detailed example, illustrating the connections to higher homotopy operations.Comment: This is the version published by Algebraic & Geometric Topology on 21 June 200

Stems and Spectral Sequences

We introduce the category Pstem[n] of n-stems, with a functor P[n] from spaces to Pstem[n]. This can be thought of as the n-th order homotopy groups of a space. We show how to associate to each simplicial n-stem Q an (n+1)-truncated spectral sequence. Moreover, if Q=P[n]X is the Postnikov n-stem of a simplicial space X, the truncated spectral sequence for Q is the truncation of the usual homotopy spectral sequence of X. Similar results are also proven for cosimplicial n-stems. They are helpful for computations, since n-stems in low degrees have good algebraic models

A universal characterization of higher algebraic K-theory

In this paper we establish a universal characterization of higher algebraic K-theory in the setting of small stable infinity categories. Specifically, we prove that connective algebraic K-theory is the universal additive invariant, i.e., the universal functor with values in spectra which inverts Morita equivalences, preserves filtered colimits, and satisfies Waldhausen's additivity theorem. Similarly, we prove that non-connective algebraic K-theory is the universal localizing invariant, i.e., the universal functor that moreover satisfies the "Thomason-Trobaugh-Neeman" localization theorem. To prove these results, we construct and study two stable infinity categories of "noncommutative motives"; one associated to additivity and another to localization. In these stable infinity categories, Waldhausen's S. construction corresponds to the suspension functor and connective and non-connective algebraic K-theory spectra become corepresentable by the noncommutative motive of the sphere spectrum. In particular, the algebraic K-theory of every scheme, stack, and ring spectrum can be recovered from these categories of noncommutative motives. In order to work with these categories of noncommutative motives, we establish comparison theorems between the category of spectral categories localized at the Morita equivalences and the category of small idempotent-complete stable infinity categories. We also explain in detail the comparison between the infinity categorical version of Waldhausen K-theory and the classical definition. As an application of our theory, we obtain a complete classification of the natural transformations from higher algebraic K-theory to topological Hochschild homology (THH) and topological cyclic homology (TC). Notably, we obtain an elegant conceptual description of the cyclotomic trace map.Comment: Various revisions and correction

Impaired Retinal Vasoreactivity: An Early Marker of Stroke Risk in Diabetes

Diabetes is a common cause of small vessel disease leading to stroke and vascular dementia. While the function and structure of large cerebral vessels can be easily studied, the brain’s microvasculature remains difficult to assess. Previous studies have demonstrated that structural changes in the retinal vessel architecture predict stroke risk, but these changes occur at late disease stages. Our goal was to examine whether retinal vascular status can predict cerebral small vessel dysfunction during early stages of diabetes. Retinal vasoreactivity and cerebral vascular function were measured in 78 subjects (19 healthy controls, 22 subjects with prediabetes, and 37 with type‐2 diabetes) using a new noninvasive retinal imaging device (Dynamic Vessel Analyzer) and transcranial Doppler studies, respectively. Cerebral blood vessel responsiveness worsened with disease progression of diabetes. Similarly, retinal vascular reactivity was significantly attenuated in subjects with prediabetes and diabetes compared to healthy controls. Subjects with prediabetes and diabetes with impaired cerebral vasoreactivity showed mainly attenuation of the retinal venous flicker response. This is the first study to explore the relationship between retinal and cerebral vascular function in diabetes. Impairment of venous retinal responsiveness may be one of the earliest markers of vascular dysfunction in diabetes possibly indicating subsequent risk of stroke and vascular dementia.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/136050/1/jon12412.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/136050/2/jon12412_am.pd

An optical-IR jet in 3C133

We report the discovery of a new optical-IR synchrotron jet in the radio galaxy 3C133 from our HST/NICMOS snapshot survey. The jet and eastern hotspot are well resolved, and visible at both optical and IR wavelengths. The IR jet follows the morphology of the inner part of the radio jet, with three distinct knots identified with features in the radio. The radio-IR SED's of the knots are examined, along with those of two more distant hotspots at the eastern extreme of the radio feature. The detected emission appears to be synchrotron, with peaks in the NIR for all except one case, which exhibits a power-law spectrum throughout.Comment: ApJ accepted. 14 pages, 6 figure