Links in classifying spaces of symmetric groups
Author: Moritz Rodenhausen
Publisher:
Published: 2010
Total Pages: 141
ISBN-13:
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Classifying Spaces of Symmetric Groups and Wreath Products
Author: David Louis Arnold
Publisher:
Published: 2013
Total Pages: 137
ISBN-13:
DOWNLOAD EBOOKThis thesis was motivated by a desire to better understand the structure of classifying spaces of symmetric groups. The results contained in this thesis fall into two categories: general results about stable splittings, or the groups we will work with, and specific results about the stable splittings completed at the prime 2. We also present two examples involving linkage. It has been hypothesized that all linkage is strong linkage: we present a counter example. It was also thought that isomorphic summands of a classifying space would either all be linked in that space or all be linked in the spaces for some collection of subgroups. Again, we identify a counter example.
Classifying Spaces of Sporadic Groups
Author: David J. Benson
Publisher: American Mathematical Soc.
Published: 2008
Total Pages: 310
ISBN-13: 0821844741
DOWNLOAD EBOOKFor each of the 26 sporadic finite simple groups, the authors construct a 2-completed classifying space using a homotopy decomposition in terms of classifying spaces of suitable 2-local subgroups. This construction leads to an additive decomposition of the mod 2 group cohomology.
Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92
Author: Ib Madsen
Publisher: Princeton University Press
Published: 2016-03-02
Total Pages: 296
ISBN-13: 1400881471
DOWNLOAD EBOOKBeginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more recent work on the maps between these spaces and the properties of the PL and Top characteristic classes, and includes integrality theorems for topological and PL manifolds. Later chapters treat the integral cohomology of BPL and Btop. The authors conclude with a discussion of the PL and topological cobordism rings and a construction of the torsion-free generators.
Introduction to Topological Quantum Matter & Quantum Computation
Author: Tudor D. Stanescu
Publisher: CRC Press
Published: 2016-12-19
Total Pages: 395
ISBN-13: 1482245949
DOWNLOAD EBOOKWhat is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and emphasizes the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the torric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Quantum computation is also presented using a broad perspective, which includes fundamental aspects of quantum mechanics, such as Bell's theorem, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and elements of classical and quantum information theory.
Invitations to Geometry and Topology
Author: Martin R. Bridson
Publisher:
Published: 2002
Total Pages: 352
ISBN-13: 9780198507727
DOWNLOAD EBOOKThis volume presents an array of topics that introduce the reader to key ideas in active areas in geometry and topology. The material is presented in a way that both graduate students and researchers should find accessible and enticing. The topics covered range from Morse theory and complex geometry theory to geometric group theory, and are accompanied by exercises that are designed to deepen the reader's understanding and to guide them in exciting directions for future investigation.
Transformation Groups
Author: Katsuo Kawakubo
Publisher: Springer
Published: 2006-11-14
Total Pages: 406
ISBN-13: 3540461787
DOWNLOAD EBOOKThe Classifying Spaces for Surgery and Cobordism of Manifolds
Author: Ib Madsen
Publisher: Princeton University Press
Published: 1979-11-21
Total Pages: 300
ISBN-13: 9780691082264
DOWNLOAD EBOOKBeginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more recent work on the maps between these spaces and the properties of the PL and Top characteristic classes, and includes integrality theorems for topological and PL manifolds. Later chapters treat the integral cohomology of BPL and Btop. The authors conclude with a discussion of the PL and topological cobordism rings and a construction of the torsion-free generators.
Topology and Representation Theory
Author: Eric M. Friedlander
Publisher: American Mathematical Soc.
Published: 1994
Total Pages: 330
ISBN-13: 0821851659
DOWNLOAD EBOOKDuring 1991-1992, Northwestern University conducted a special emphasis year on the topic, "The connections between topology and representation theory." Activities over the year culminated in a conference in May 1992 which attracted over 120 participants. Most of the plenary lectures at the conference were expository and designed to introduce current trends to graduate students and nonspecialists familiar with algebraic topology. This volume contains refereed papers presented or solicited at the conference; one paper is based on a seminar given during the emphasis year.
Knots, Links, Spatial Graphs, and Algebraic Invariants
Author: Erica Flapan
Publisher: American Mathematical Soc.
Published: 2017-05-19
Total Pages: 202
ISBN-13: 1470428474
DOWNLOAD EBOOKThis volume contains the proceedings of the AMS Special Session on Algebraic and Combinatorial Structures in Knot Theory and the AMS Special Session on Spatial Graphs, both held from October 24–25, 2015, at California State University, Fullerton, CA. Included in this volume are articles that draw on techniques from geometry and algebra to address topological problems about knot theory and spatial graph theory, and their combinatorial generalizations to equivalence classes of diagrams that are preserved under a set of Reidemeister-type moves. The interconnections of these areas and their connections within the broader field of topology are illustrated by articles about knots and links in spatial graphs and symmetries of spatial graphs in and other 3-manifolds.
