Twisted Alexander polynomials and incompressible surfaces given by ideal points

We study incompressible surfaces constructed by Culler-Shalen theory in the context of twisted Alexander polynomials. For a $1$st cohomology class of a $3$-manifold the coefficients of twisted Alexander polynomials induce regular functions on the $SL_2(\mathbb{C})$-character variety. We prove that if an ideal point gives a Thurston norm minimizing non-separating surface dual to the cohomology class, then the regular function of the highest degree has a finite value at the ideal point.Comment: 10 pages, to appear in "The special issue for the 20th anniversary", the Journal of Mathematical Sciences, the University of Toky

The virtual fibering theorem for 3-manifolds

In 2007 Agol showed that if N is an aspherical compact 3-manifold with empty or toroidal boundary such that its fundamental group is virtually RFRS, then $N$ is virtually fibered. We give a largely self-contained proof of Agol's theorem using complexities of sutured manifolds.Comment: 25 pages, 6 figures v3: slightly revised an argument, otherwise minor change

Culture, Mind, and the Brain: Current Evidence and Future Directions

Current research on culture focuses on independence and interdependence and documents numerous East-West psychological differences, with an increasing emphasis placed on cognitive mediating mechanisms. Lost in this literature is a time-honored idea of culture as a collective process composed of cross-generationally transmitted values and associated behavioral patterns (i.e., practices). A new model of neuro-culture interaction proposed here addresses this conceptual gap by hypothesizing that the brain serves as a crucial site that accumulates effects of cultural experience, insofar as neural connectivity is likely modified through sustained engagement in cultural practices. Thus, culture is “embrained,” and moreover, this process requires no cognitive mediation. The model is supported in a review of empirical evidence regarding (a) collective-level factors involved in both production and adoption of cultural values and practices and (b) neural changes that result from engagement in cultural practices. Future directions of research on culture, mind, and the brain are discussed