Finite covers of random 3-manifolds

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model of random 3-manifold, we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds. Our results contrast with the analogous probabilities for groups coming from random balanced presentations, giving quantitative theorems to the effect that 3-manifold groups have many more finite quotients than random groups. The next natural question is whether these covers have positive betti number. For abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show that the probability of positive betti number is 0. In fact, many of these questions boil down to questions about the mapping class group. We are lead to consider the action of mapping class group of a surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show that if the genus of S is large, then this action is very mixing. In particular, the action factors through the alternating group of each orbit. This is analogous to Goldman's theorem that the action of the mapping class group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio

Critic-proofing

Heuristic evaluation – a technique where experts inspect software and determine where the application violates predetermined policies for good usability – is an effective technique for evaluating productivity software. The technique has recently been applied to video games, examining playability and usability for both single and multiplayer games. However, the severity ratings assigned to usability problems and used as a coarse categorization method for triage are still subjectively and somewhat arbitrarily assigned by evaluators, offering limited organizational value. In addition, they fail to account for the diversity found between games and game genres. In this paper we present a modified heuristic evaluation technique, which produces a prioritized list of heuristic violations based on the problem’s frequency, impact, persistence, the heuristic it violates, and the game’s genre. We evaluate our technique in a case study and show that the technique provides substantial value with little additional effort

Gemini: A Pervasive Accumulated Context Exergame

Exergames encourage physical activity, but generally require specialized hardware and prescribed activities; whereas pervasive accumulated context exergames (PACEs) allow players to choose their type of exercise, but have limited depth of play. For mass commercialization of PACEs, facilitating long-term behavioural change, we propose two requirements: that PACEs support large-scale and flexible deployment; and that the design of PACEs support staying power through long-term playability. From these requirements, we motivate six PACE design principles and use these principles to develop a multiplayer roleplaying PACE. Results from a week-long study of our game showed that by satisfying the six design principles, we can create a PACE with scalability and staying power. Our results are the first step toward creating PACEs that promotes long-term game engagement, which is needed for activity-related behaviour change.Ye