John W. Morgan – författare

The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.

Native temperate grasslands are Australia’s most threatened ecosystems. Grasslands have been eliminated from across much of their former extent and continue to be threatened by urban expansion, agricultural intensification, weed invasion and the uncertain impacts of climate change. Research, however, is showing us new ways to manage grasslands, and techniques for restoration are advancing. The importance of ongoing stewardship also means it is vital to develop new strategies to encourage a broader cross-section of society to understand and appreciate native grasslands and their ecology.

Land of Sweeping Plains synthesises the scientific literature in a readily accessible manner and includes a wealth of practical experience held by policy makers, farmers, community activists and on-ground grassland managers. It aims to provide all involved in grassland management and restoration with the technical information necessary to conserve and enhance native grasslands. For readers without the responsibility of management, such as students and those interested in biodiversity conservation, it provides a detailed understanding of native grassland ecology, management challenges and solutions and, importantly, inspiration to engage with this critically endangered ecosystem.

Practical, easy to read and richly illustrated, this book brings together the grassland knowledge of experts in ethnobotany, ecology, monitoring, planning, environmental psychology, community engagement, flora and fauna management, environmental restoration, agronomy, landscape architecture and urban design.