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Author:   Stefan Behrens (Assistant Professor, Assistant Professor, Bielefeld University) ,  Boldizsar Kalmar (Assistant Professor, Assistant Professor, Budapest University of Technology and Economics) ,  Min Hoon Kim (Assistant Professor, Assistant Professor, Chonnam National University) ,  Mark Powell (Durham University, Durham University, Associate Professor)
Publisher:   Oxford University Press
Imprint:   Oxford University Press
Dimensions:   Width: 16.00cm , Height: 3.00cm , Length: 24.30cm
Weight:   0.944kg
ISBN:  

9780198841319

ISBN 10:   0198841310
Pages:   496
Publication Date:   20 July 2021
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us.

Table of Contents

Preface 1: Context for the disc embedding theorem 2: Outline of the upcoming proof Part 1: Decomposition space theory 3: The Schoenflies theorem after Mazur, Morse, and Brown 4: Decomposition space theory and the Bing shrinking criterion 5: The Alexander gored ball and the Bing decomposition 6: A decomposition that does not shrink 7: The Whitehead decomposition 8: Mixed Bing-Whitehead decompositions 9: Shrinking starlike sets 10: The ball to ball theorem Part II: Building skyscrapers 11: Intersection numbers and the statement of the disc embedding theorem 12: Gropes, towers, and skyscrapers 13: Picture camp 14: Architecture of infinite towers and skyscrapers 15: Basic geometric constructions 16: From immersed discs to capped gropes 17: Grope height raising and 1-storey capped towers 18: Tower height raising and embedding Part III: Interlude 19: Good groups 20: The s-cobordism theorem, the sphere embedding theorem, and the Poincaré conjecture 21: The development of topological 4-manifold theory 22: Surgery theory and the classification of closed, simply connected 4-manifolds 23: Open problems Part IV: Skyscrapers are standard 24: Replicable rooms and boundary shrinkable skyscrapers 25: The collar adding lemma 26: Key facts about skyscrapers and decomposition space theory 27: Skyscrapers are standard: an overview 28: Skyscrapers are standard: the details Bibliography Afterword Index

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Author Information

Dr Stefan Behrens is an assistant professor in the Geometry and Topology group led by Prof. Dr. Stefan Bauer. His field of research is low dimensional topology, with a focus on the topology of smooth 4-manifolds. Boldizsar Kalmar was a research assistant at the Alfred Renyi Institute of Mathematics in 2005, then he got his PhD at Kyushu University in Japan in 2008. Then he did research at the Alfred Renyi Institute of Mathematics until 2017. He visited the Max Planck Institute for Mathematics in 2013. His research field is the topology of singular maps and low dimensional topology. Dr Mark Powell obtained his PhD from the University of Edinburgh under the supervision of Andrew Ranicki in 2011. After positions at Indiana University, the Max Planck Institute in Bonn, and at UQAM in Montreal, he moved to Durham University in 2017 to take up a position as Associate Professor. Dr Arunima Ray received a PhD in mathematics from Rice University, in Houston, USA in 2014 and subsequently held a postdoctoral fellowship at Brandeis University at Waltham, USA. She is currently a Lise Meitner group leader at the Max Planck Institute for Mathematics in Bonn, Germany. Her research is in low-dimensional topology, specifically the study of knots and links, and 3- and 4-manifolds.

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