Chemical Topology, Tilings and Entanglement

This book introduces low-dimensional geometry and topology to chemists and materials scientists in an accessible, visual style and will be of interest to structural chemists interested in understanding the complexity of entanglements.

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Structural entanglement in molecular graphs and nets is relevant to many chemical materials, from fullerenes and associated sp2 carbon materials to DNA complexes and metal-organic frameworks. This book introduces tangled finite and infinite nets that are useful to describe chemical structures. It brings modern low-dimensional geometry and topology to chemists and materials scientists in an accessible, visual style with mathematical and topological concepts richly illustrated and translated to chemical systems. Chapters introduce concepts and structures stepwise from simpler to more complex examples.
The key concepts discussed are two-dimensional topology versus geometry and reticulations of surfaces of varying topology as a means to generate and describe tangled structures. Orbifolds, knot theory and chirality are analysed as modern approaches to symmetry, concepts that were pioneered by the authors of this book. Whilst explaining the most recent findings and theories in this active field and detailing the important and novel mathematics underlying these new approaches to entanglement, the book maintains a focus on the latest chemical applications.
This book will be of interest to advanced students structural chemists interested in understanding the complexity of entanglements, as well as inorganic and supramolecular chemists, chemical engineers, crystallographers and mathematicians.