Topology: A Geometric Approach

The ways in which organizations make use of information available to them to make decisions and manage activity is an essential topic of investigation for human factors. When the information is uncertain, incomplete or subject to change, then decision making and activity management can become challenging. Under such circumstances, it has become commonplace to use the concept of sensemaking as the lens through which to view organizational behavior. This book offers a unique perspective on sensemaking through its consideration of the variety of ways in which Incident Response is managed by the Police. As an incident moves from the initial call handling to subsequent mobilization of response to first officer attending, a wide range of information is acquired, processed and shared, and the organization (and individuals who work within it) face challenges of making sense of the situation to which they are responding. Moving from routine incidents to large-scale emergencies, the authors explore how sensemaking is influenced and affected by the challenges of interoperability within and between organizations. In addition, the book develops a view of sensemaking which draws on the theory of distributed cognition, focusing in particular on the question of how the technology that is available to Police personnel can support (and sometimes thwart) their ability to make sense of the unfolding situation. The main argument in this book is that sensemaking is distributed cognition, and that cognitive processes involved in sensemaking are mediated through interactions with artifacts and other agents. Three perspectives of sensemaking as distributed cognition are presented: making sense with artifacts, making sense through artifacts, and making sense through collaboration.The book gives an introduction to topology at the advanced undergraduate to beginning graduate level, with an emphasis on its geometric aspects. Part I contains three chapters on basic point set topology, classification of surfaces via handle decompositions, and the fundamental group appropriate for a one semester or two quarter course. Carefully developed exercise sets support high student involvement. Besides exercises embedded within a chapter, there areextensive supplementary exercises to extend the material. Surfaces occur as key examples in treatments of the fundamental group, covering spaces, CW complexes, and homology in the last four chapters. Each chapter of Part I ends with a substantial project. Part II is written in a problem based format. These problems contain appropriate hints and background material to enable the student to work through the basic theory of covering spaces, CW complexes, and homology with the instructor's guidance. Low dimensional cases provide motivation and examples for the general development, with an emphasis on treating geometric ideas first encountered in Part I such as orientation. Part II allows the book to be used for a year long course at the firstyear graduate level.The book's collection of over 750 exercises range from simple checks of omitted details in arguments, to reinforce the material and increase student involvement, to the development of substantial theorems that have been broken into many steps. The style encourages an active student role. Solutions to selected exercises are included as an appendix. Solutions to all exercises are available to the instructor in electronic form.This text forms the latest in the Oxford Graduate Texts in Mathematics series which publishes textbooks suitable for graduate students in mathematics and its applications. The level of books may range from some suitable for advanced undergraduate courses at one end, to others of interest to research workers. The emphasis is on texts of high mathematical quality in active areas, particularly areas that are not well represented in the literature at present.