Frontiers In Geometry And Topology
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Frontiers in Geometry and Topology
Author: Paul M. N. Feehan
language: en
Publisher: American Mathematical Society
Release Date: 2024-07-19
This volume contains the proceedings of the summer school and research conference “Frontiers in Geometry and Topology”, celebrating the sixtieth birthday of Tomasz Mrowka, which was held from August 1–12, 2022, at the Abdus Salam International Centre for Theoretical Physics (ICTP). The summer school featured ten lecturers and the research conference featured twenty-three speakers covering a range of topics. A common thread, reflecting Mrowka's own work, was the rich interplay among the fields of analysis, geometry, and topology. Articles in this volume cover topics including knot theory; the topology of three and four-dimensional manifolds; instanton, monopole, and Heegaard Floer homologies; Khovanov homology; and pseudoholomorphic curve theory.
Geometry and Topology Down Under
Author: Craig D. Hodgson
language: en
Publisher: American Mathematical Soc.
Release Date: 2013-08-23
This book contains the proceedings of the conference Geometry & Topology Down Under, held July 11-22, 2011, at the University of Melbourne, Parkville, Australia, in honour of Hyam Rubinstein. The main topic of the book is low-dimensional geometry and topology. It includes both survey articles based on courses presented at the conferences and research articles devoted to important questions in low-dimensional geometry. Together, these contributions show how methods from different fields of mathematics contribute to the study of 3-manifolds and Gromov hyperbolic groups. It also contains a list of favorite problems by Hyam Rubinstein.
Topology: Unravelling the Fabric of Space
Author: Pasquale De Marco
language: en
Publisher: Pasquale De Marco
Release Date: 2025-04-20
Embark on a captivating journey through the world of topology with Topology: Unravelling the Fabric of Space, a comprehensive guide that unveils the intricate beauty and profound insights of this fascinating mathematical discipline. Discover how topology unravels the fabric of space, providing a framework for understanding the structure of our universe and beyond. Delve into the fundamental concepts of topology, exploring the properties of geometric figures that remain unchanged under continuous deformations. Uncover the significance of topological spaces, homeomorphisms, and homology, and witness how these concepts lay the foundation for understanding the structure and behavior of shapes and spaces. Explore the realm of topological invariants, numerical measures that capture the essence of geometric objects. Learn how these invariants enable mathematicians to classify and compare different shapes and spaces, providing deep insights into their underlying structure. Discover the applications of topological invariants in diverse fields, from physics and engineering to computer science and biology. Witness the power of topology in unraveling the mysteries of the physical world. Delve into the geometry of spacetime, the fundamental fabric of our universe, and understand how topology provides insights into the behavior of elementary particles, the structure of atoms, and the properties of black holes. Discover the profound impact of topology on computer science, where it finds applications in computer graphics, image processing, and network analysis. Explore how topological algorithms efficiently represent and manipulate complex data structures, optimize routing protocols, and design efficient algorithms for solving computational problems. Topology: Unravelling the Fabric of Space is an indispensable resource for students, researchers, and anyone fascinated by the intricate world of shapes and spaces. Its comprehensive coverage of fundamental concepts, theorems, and applications makes it an invaluable guide to the captivating realm of topology. If you like this book, write a review on google books!