Eeting Infinity

Meeting Infinity

Hyperbolic Knot Theory

This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic structure on a knot complement in the 3-sphere gives a complete knot invariant. However, it remains a difficult problem to relate the hyperbolic geometry of a knot to other invariants arising from knot theory. In particular, it is difficult to determine hyperbolic geometric information from a knot diagram, which is classically used to describe a knot. This textbook provides background on these problems, and tools to determine hyperbolic information on knots. It also includes results and state-of-the art techniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. Some experience with some differential topology and Riemannian geometry will also be helpful.

300 Mindfulness Exercises and Activities

Discover 300 ways to practice mindfulness and bring calm, clarity, and balance into your life—one moment at a time. Whether you're new to mindfulness or a seasoned practitioner, 300 Mindfulness Exercises and Activities offers a rich collection of simple, effective techniques to reduce stress, improve focus, and support mental and emotional well-being. Inside this comprehensive guide, you'll find a wide variety of exercises—from quick breathing techniques and grounding practices to mindful journaling prompts, movement-based activities, and more. Each practice is designed to help you stay present, manage anxiety, and build resilience in everyday life. Perfect for individuals, coaches, therapists, teachers, and anyone seeking personal growth, this book is your go-to resource for creating a consistent mindfulness practice—whether you have five minutes or an entire hour. In this book, you’ll discover: • Practical tools to ease stress and quiet the mind • Simple ways to improve focus, clarity, and emotional balance • Adaptable practices for individuals, groups, or client sessions • Exercises for mornings, work breaks, bedtime, and everything in between • A flexible structure that lets you choose what you need—when you need it most Whether you're looking to calm your racing thoughts, deepen your meditation practice, or lead others through mindfulness, this book gives you the tools to do it—all in one place. Start practicing mindfulness today—and feel the difference it makes.