Higher categories, colimits, and the blob complex

We summarize our axioms for higher categories, and describe the blob complex. Fixing an n-category C, the blob complex associates a chain complex B_*(W;C)$ to any n-manifold W. The 0-th homology of this chain complex recovers the usual topological quantum field theory invariants of W. The higher homology groups should be viewed as generalizations of Hochschild homology (indeed, when W=S^1 they coincide). The blob complex has a very natural definition in terms of homotopy colimits along decompositions of the manifold W. We outline the important properties of the blob complex, and sketch the proof of a generalization of Deligne's conjecture on Hochschild cohomology and the little discs operad to higher dimensions.Comment: 7 page

The centre of the extended Haagerup subfactor has 22 simple objects

We explain a technique for discovering the number of simple objects in $Z(C)$, the center of a fusion category $C$, as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring $K(C)$ and the dimension function $K(C) \to \mathbb{C}$. The method is not guaranteed to succeed (it may give spurious answers besides the correct one, or it may simply take too much computer time), but it seems it often does. We illustrate by showing that there are 22 simple objects in the center of the extended Haagerup subfactor [arXiv:0909.4099].Comment: 10 page

Hospitality studies and hospitality management: a symbiotic relationship

The key contribution of this paper is to critically analyse advances made since the introduction of hospitality as a higher education subject, to capture contemporary thinking, and to support the recognition of the intellectual benefits for hospitality management theory and practices of a curriculum informed from a social science-based studies perspective. The benefits of this inter-relationship are demonstrated through the inclusion of an illustration informed by historical means of enquiry, which applies hermeneutical analysis and interpretation of St. Benedict's Rule (c. 530 A.D.). This serves to tangibly demonstrate the academic rigour, value, and educational gains achievable through a symbiotic relationship between hospitality studies and hospitality management

Government spending and re-election: Quasi-experimental evidence from Brazilian municipalities

Does additional government spending improve the electoral chances of incumbent political parties? This paper provides the first quasi-experimental evidence on this question. Our research design exploits discontinuities in federal funding to local governments in Brazil around several population cutoffs over the period 1982-1985. We show that extra fiscal transfers resulted in a 20% increase in local government spending per capita, and an increase of about 10 percentage points in the re-election probability of local incumbent parties. In the context of an agency model of electoral accountability, as well as existing results indicating that the revenue jumps studied here had positive impacts on education outcomes and earnings, these results suggest that expected electoral rewards encouraged incumbents to spend additional funds in ways that were valued by voters.Government spending, voting, regression discontinuity.

Communicating Climate Change: A Literature Review

For climate scientists, climate change is a problem that has a significant chance of having catastrophic environmental, social and economic consequences during the course of this century. In contrast, public opinion seems to regard with scepticism the pronouncements on climate change that emanate from the scientific community. Why the difference? This is what our research project was designed to examine. Or to put it another way: Assuming that the scientific information is correct, and that without a dramatic change in technology (and policy to promote such a change) there would be a significant risk of man-made, global catastrophe, what must be done to communicate this urgent issue to the public? We have approached the analysis of this problem by reviewing the literature on communicating climate change. By organising the literature according to the role of the major groups of participants in the information transfer process, useful insights can be gleaned. These groups include scientists, business, the government, the media and the general public. This analysis leads to an overall model of the information transfer process that highlights various issues including the role that the media plays as a lens through which the public observes scientific results.Climate change, media, scientists, business, government, the general public, literature review, Environmental Economics and Policy, Marketing, Resource /Energy Economics and Policy, 1402,

Man and machine thinking about the smooth 4-dimensional Poincar\'e conjecture

While topologists have had possession of possible counterexamples to the smooth 4-dimensional Poincar\'{e} conjecture (SPC4) for over 30 years, until recently no invariant has existed which could potentially distinguish these examples from the standard 4-sphere. Rasmussen's s-invariant, a slice obstruction within the general framework of Khovanov homology, changes this state of affairs. We studied a class of knots K for which nonzero s(K) would yield a counterexample to SPC4. Computations are extremely costly and we had only completed two tests for those K, with the computations showing that s was 0, when a landmark posting of Akbulut (arXiv:0907.0136) altered the terrain. His posting, appearing only six days after our initial posting, proved that the family of ``Cappell--Shaneson'' homotopy spheres that we had geared up to study were in fact all standard. The method we describe remains viable but will have to be applied to other examples. Akbulut's work makes SPC4 seem more plausible, and in another section of this paper we explain that SPC4 is equivalent to an appropriate generalization of Property R (``in S^3, only an unknot can yield S^1 x S^2 under surgery''). We hope that this observation, and the rich relations between Property R and ideas such as taut foliations, contact geometry, and Heegaard Floer homology, will encourage 3-manifold topologists to look at SPC4.Comment: 37 pages; changes reflecting that the integer family of Cappell-Shaneson spheres are now known to be standard (arXiv:0907.0136

The blob complex

Given an n-manifold M and an n-category C, we define a chain complex (the "blob complex") B_*(M;C). The blob complex can be thought of as a derived category analogue of the Hilbert space of a TQFT, and as a generalization of Hochschild homology to n-categories and n-manifolds. It enjoys a number of nice formal properties, including a higher dimensional generalization of Deligne's conjecture about the action of the little disks operad on Hochschild cochains. Along the way, we give a definition of a weak n-category with strong duality which is particularly well suited for work with TQFTs.Comment: 106 pages. Version 3 contains many improvements following suggestions from the referee and others, and some additional materia

Fixing the functoriality of Khovanov homology

We describe a modification of Khovanov homology (math.QA/9908171), in the spirit of Bar-Natan (math.GT/0410495), which makes the theory properly functorial with respect to link cobordisms. This requires introducing `disorientations' in the category of smoothings and abstract cobordisms between them used in Bar-Natan's definition. Disorientations have `seams' separating oppositely oriented regions, coming with a preferred normal direction. The seams satisfy certain relations (just as the underlying cobordisms satisfy relations such as the neck cutting relation). We construct explicit chain maps for the various Reidemeister moves, then prove that the compositions of chain maps associated to each side of each of Carter and Saito's movie moves (MR1238875, MR1445361) always agree. These calculations are greatly simplified by following arguments due to Bar-Natan and Khovanov, which ensure that the two compositions must agree, up to a sign. We set up this argument in our context by proving a result about duality in Khovanov homology, generalising previous results about mirror images of knots to a `local' result about tangles. Along the way, we reproduce Jacobsson's sign table (math.GT/0206303) for the original `unoriented theory', with a few disagreements.Comment: 91 pages. Added David Clark as co-author. Further detail on variations of third Reidemeister moves, to allow treatment of previously missing cases of movie move six. See changelog section for more detai