Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces

Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces
Author :
Publisher : Springer
Total Pages : 148
Release :
ISBN-10 : 9783319115177
ISBN-13 : 3319115170
Rating : 4/5 (77 Downloads)

Synopsis Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces by : Marek Golasiński

This is a monograph that details the use of Siegel’s method and the classical results of homotopy groups of spheres and Lie groups to determine some Gottlieb groups of projective spaces or to give the lower bounds of their orders. Making use of the properties of Whitehead products, the authors also determine some Whitehead center groups of projective spaces that are relevant and new within this monograph.

Algebraic Topology and Related Topics

Algebraic Topology and Related Topics
Author :
Publisher : Springer
Total Pages : 318
Release :
ISBN-10 : 9789811357428
ISBN-13 : 9811357420
Rating : 4/5 (28 Downloads)

Synopsis Algebraic Topology and Related Topics by : Mahender Singh

This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.

Mathematical Reviews

Mathematical Reviews
Author :
Publisher :
Total Pages : 1884
Release :
ISBN-10 : UVA:X006195258
ISBN-13 :
Rating : 4/5 (58 Downloads)

Synopsis Mathematical Reviews by :

Algebraic and Geometric Surgery

Algebraic and Geometric Surgery
Author :
Publisher : Oxford University Press
Total Pages : 396
Release :
ISBN-10 : 0198509243
ISBN-13 : 9780198509240
Rating : 4/5 (43 Downloads)

Synopsis Algebraic and Geometric Surgery by : Andrew Ranicki

This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students, who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, co-bordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.

Fibrewise Homotopy Theory

Fibrewise Homotopy Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 344
Release :
ISBN-10 : 9781447112655
ISBN-13 : 1447112652
Rating : 4/5 (55 Downloads)

Synopsis Fibrewise Homotopy Theory by : Michael Charles Crabb

Topology occupies a central position in modern mathematics, and the concept of the fibre bundle provides an appropriate framework for studying differential geometry. Fibrewise homotopy theory is a very large subject that has attracted a good deal of research in recent years. This book provides an overview of the subject as it stands at present.

On Thom Spectra, Orientability, and Cobordism

On Thom Spectra, Orientability, and Cobordism
Author :
Publisher : Springer Science & Business Media
Total Pages : 593
Release :
ISBN-10 : 9783540777519
ISBN-13 : 3540777512
Rating : 4/5 (19 Downloads)

Synopsis On Thom Spectra, Orientability, and Cobordism by : Yu. B. Rudyak

Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories). These are all framed by (co)homology theories and spectra. The author has also performed a service to the history of science in this book, giving detailed attributions.

Homotopical Topology

Homotopical Topology
Author :
Publisher : Springer
Total Pages : 635
Release :
ISBN-10 : 9783319234885
ISBN-13 : 3319234889
Rating : 4/5 (85 Downloads)

Synopsis Homotopical Topology by : Anatoly Fomenko

This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain. Therefore, this updated English edition will be much welcomed by the mathematical community. Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences. The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).

The Norm Residue Theorem in Motivic Cohomology

The Norm Residue Theorem in Motivic Cohomology
Author :
Publisher : Princeton University Press
Total Pages : 316
Release :
ISBN-10 : 9780691191041
ISBN-13 : 0691191042
Rating : 4/5 (41 Downloads)

Synopsis The Norm Residue Theorem in Motivic Cohomology by : Christian Haesemeyer

This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky’s proof and introduce the key figures behind its development. They proceed to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. The book then addresses symmetric powers of motives and motivic cohomology operations. Comprehensive and self-contained, The Norm Residue Theorem in Motivic Cohomology unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.

Stable Stems

Stable Stems
Author :
Publisher : American Mathematical Soc.
Total Pages : 174
Release :
ISBN-10 : 9781470437886
ISBN-13 : 1470437880
Rating : 4/5 (86 Downloads)

Synopsis Stable Stems by : Daniel C. Isaksen

The author presents a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. He uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over C through the 70-stem. He then uses the motivic Adams spectral sequence to obtain motivic stable homotopy groups through the 59-stem. He also describes the complete calculation to the 65-stem, but defers the proofs in this range to forthcoming publications. In addition to finding all Adams differentials, the author also resolves all hidden extensions by 2, η, and ν through the 59-stem, except for a few carefully enumerated exceptions that remain unknown. The analogous classical stable homotopy groups are easy consequences. The author also computes the motivic stable homotopy groups of the cofiber of the motivic element τ. This computation is essential for resolving hidden extensions in the Adams spectral sequence. He shows that the homotopy groups of the cofiber of τ are the same as the E2-page of the classical Adams-Novikov spectral sequence. This allows him to compute the classical Adams-Novikov spectral sequence, including differentials and hidden extensions, in a larger range than was previously known.