Derived Categories And The Analytic Approach To General Reciprocity Laws. Part Iii,
2010
Loyola Marymount University
Derived Categories And The Analytic Approach To General Reciprocity Laws. Part Iii, Michael Berg
Mathematics, Statistics and Data Science Faculty Works
Building on the scaffolding constructed in the first two articles in this series, we now proceed to the geometric phase of our sheaf (-complex) theoretic quasidualization of Kubota's formalism for n-Hilbert reciprocity. Employing recent work by Bridgeland on stability conditions, we extend our yoga of t-structures situated above diagrams of specifically designed derived categories to arrangements of metric spaces or complex manifolds. This prepares the way for proving n-Hilbert reciprocity by means of singularity analysis.
Algorithms For Upper Bounds Of Low Dimensional Group Homology,
2010
University of Kentucky
Algorithms For Upper Bounds Of Low Dimensional Group Homology, Joshua D. Roberts
University of Kentucky Doctoral Dissertations
A motivational problem for group homology is a conjecture of Quillen that states, as reformulated by Anton, that the second homology of the general linear group over R = Z[1/p; ζp], for p an odd prime, is isomorphic to the second homology of the group of units of R, where the homology calculations are over the field of order p. By considering the group extension spectral sequence applied to the short exact sequence 1 → SL2 → GL2 → GL1 → 1 we show that the calculation of the homology …
On The Integrability Of Orthogonal Distributions In Poisson Manifolds,
2010
Portland State University
On The Integrability Of Orthogonal Distributions In Poisson Manifolds, Daniel Fish, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
We study conditions for the integrability of the distribution defined on a regular Poisson manifold as the orthogonal complement (with respect to some (pseudo)-Riemannian metric) to the tangent spaces of the leaves of a symplectic foliation. Examples of integrability and non-integrability of this distribution are provided.
