Reflection positivity and invertible topological phases

We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable homotopy theory. We apply these field theory considerations to lattice systems, assuming the existence and validity of low energy effective field theory approximations, and thereby produce a general formula for the group of Symmetry Protected Topological (SPT) phases in terms of Thom's bordism spectra; the only input is the dimension and symmetry group. We provide computations for fermionic systems in physically relevant dimensions. Other topics include symmetry in quantum field theories, a relativistic 10-fold way, the homotopy theory of relativistic free fermions, and a topological spin-statistics theorem.Comment: 136 pages, 16 figures; minor changes/corrections in version 2; v3 major revision; v4 minor revision: corrected proof of Lemma 9.55, many small changes throughout; v5 version for publication in Geometry & Topolog

Past Place, Present Prejudice: The Impact of Adolescent Racial Context on White Racial Attitudes

Extensive research on racial contexts suggests that white Americans living near black Americans adopt more negative racial attitudes. Theoretically, local intergroup exposure has been conceptualized as acting contemporaneously through various mechanisms. However, a separate body of research on political socialization indicates that adolescent experiences are often especially influential. We hypothesize that whites’ racial contexts during adolescence produce prejudiced responses. We then test this hypothesis using two complementary data sets, a population-based panel conducted 2007–13 and the Youth-Parent Socialization Panel Survey (1965–97). Our analyses demonstrate the enduring influence of adolescent contexts at larger levels of aggregation: while the racial composition of whites’ current counties is not a consistent predictor of racial prejudice, the racial composition of their county during high school is. Proximity during one’s formative years increases racial prejudice years later, providing new insights about local contextual effects and the roots of racial prejudice

Loop groups and twisted K-theory I

This is the first in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the "Verlinde ring" of its loop group. In this paper we set up the foundations of twisted equivariant K-groups, and more generally twisted K-theory of groupoids. We establish enough basic properties to make effective computations. Using the Mayer-Vietoris spectral sequence we compute the twisted equivariant K-groups of a compact connected Lie group G with torsion free fundamental group. We relate this computation to the representation theory of the loop group at a level related to the twisting