Hodge filtered complex bordism

We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural generalization of Deligne cohomology. For smooth complex algebraic varieties, we show that the theory satisfies a projective bundle formula and \A^1-homotopy invariance. Moreover, we obtain transfer maps along projective morphisms.Comment: minor revision; final version accepted for publication by the Journal of Topolog

Open Source or Off-the-Shelf?:Establishing an institutional repository for a small institution

Effective management of digital assets as well as increasing research exposure and impact are particular challenges faced by smaller institutions with limited infrastructure and resources. The paper explores the significant factors involved in considering, planning and establishing an institutional repository for Bond University, one of the smaller higher education providers in Australia. The salient benefits and advantages as well as the disadvantages of implementing an off-the-shelf product as opposed to an open source solution for an institutional repository are compared. The rationale for choosing a proprietary product over an open source solution is discussed, as well as the process for obtaining funding and the support of key stakeholders within the University. The paper describes the strategies employed to populate the repository retrospectively and to train academic staff and researchers in self-archiving. The development of policy governing the repository and intellectual property and copyright implications are also covered. Background on Bond Universit

Algorithm 830: Another Visit With Standard and Modified Givens Transformations and A Remark on Algorithm 539

First we report on a correction and improvement to the Level 1 Blas routine srotmg for computing the Modified Givens Transformation (MG). We then, in the light of the performance of the code on modern compiler/hardware combinations, reconsider the strategy of supplying separate routines to compute and apply the transformation. Finally, we show that the apparent savings in multiplies obtained by using MG rather than the Standard Givens Transformation (SG) do not always translate into reductions in execution time

Higher real K-theories and topological automorphic forms

Given a maximal finite subgroup G of the nth Morava stabilizer group at a prime p, we address the question: is the associated higher real K-theory EO_n a summand of the K(n)-localization of a TAF-spectrum associated to a unitary similitude group of type U(1,n-1)? We answer this question in the affirmative for p in {2, 3, 5, 7} and n = (p-1)p^{r-1} for a maximal finite subgroup containing an element of order p^r. We answer the question in the negative for all other odd primary cases. In all odd primary cases, we to give an explicit presentation of a global division algebra with involution in which the group G embeds unitarily.Comment: 37 pages. v2 contains several minor revision

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