This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell-Jones conjectures, and the other on ends of spaces and groups. In 2010-2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.

This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell-Jones conjectures, and the other on ends of spaces and groups. In 2010-2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.

"The Geometry and Topology of Coxeter Groups" is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincare Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures."

Strongholds are imaginary castles, lofty things, high barriers that separate us from the knowledge of God. Illusions built upon agreements with lies. The thing is: they look real. They feel real. When we are in agreement with the enemy of God, without even understanding why, we can end up walking in the illusion of bondage, despair and defeat. Imaginary Castles: Understanding and Pulling Down Strongholds is an easy-to-read teaching on a crucial topic for the body of Christ. You will learn: How the enemy uses lies and deception to build strongholds. How to recognize and destroy strongholds in your life. How to prevent strongholds from forming in the first place. How to help your loved ones get free from the illusion of bondage. Author Michael W. Davis is the founder and president of Brothers And Sisters In Christ (B.A.S.I.C.) Ministries. He enjoys camping, backpacking, playing paintball, and praise music. Michael resides in Greenwood, SC with his wife Linda, daughter Breanna, an ugly dog, and an arrogant little cat. He also has two adult children that have left the nest: Gwendolyn and Stephen.

Strongholds are imaginary castles, lofty things, high barriers that separate us from the knowledge of God. Illusions built upon agreements with lies. The thing is: they look real. They feel real. When we are in agreement with the enemy of God, we can end up walking in the illusion of bondage, despair and defeat. Michael W. Davis "has done an excellent job, creating a very strong teaching about strongholds, how to identify them and how to get rid of them. It is well supported by biblical references to further emphasize this easy-to-read, yet crucial topic for the body of Christ." Xulon Press Editorial Review You will learn: - How the enemy uses lies and deception to build strongholds. - How to recognize and destroy strongholds in your life. - How to prevent strongholds from forming in the first place. - How to help your loved ones get free from the illusion of bondage. What Readers Are Saying: "This is a fresh, easy to read book with scripture backing almost every thought. When we can identify what a stronghold is, then we can begin to tear them down one by one with the TRUTH of God's Holy Word Every Christian new and old, every lost & hurting person, leader and layman should read this book " Kimberly W. "A great read, well worth having on hand. 'Imaginary Castles' helped me understand some things in my life that I previously just didn't get." Wayne E. "I read it in one night. It's an excellent book. Very good for the struggling Christian or even a non-Christian looking for a good read. This book shows an in depth look into the struggles of 'bringing down strongholds', but he breaks it down in a simple way that is very easily understood by anyone. I suggest everyone should read this." Gwen D. "I am not much on reading books, let alone finishing one. 'Imaginary Castles' is one that I could not put down. I highly recommend Imaginary Castles to every believer in Jesus Christ. Read this book and live a victorious life in Christ " Wanda D. The essence... the very core of walking with God is this: Truth versus lies. One must choose each moment to either agree with the Truth of God's Word and experience the Reality of Victory, or agree with the lies of the enemy and walk in the illusion of defeat.