Since the subject of Groups of Self-Equivalences was first discussed in 1958 in a paper of Barcuss and Barratt, a good deal of progress has been achieved. This is reviewed in this volume, first by a long survey article and a presentation of 17 open problems together with a bibliography of the subject, and by a further 14 original research articles.
This volume offers the proceedings from the workshop held at the University of Milan (Italy) on groups of homotopy self-equivalences and related topics. The book comprises the articles relating current research on the group of homotopy self-equivalences, homotopy of function spaces, rational homotopy theory, classification of homotopy types, and equivariant homotopy theory. Mathematicians from many areas of the globe attended the workshops to discuss their research and to share ideas. Included are two specially-written articles, by J.W. Rutter, reviewing the work done in the area of homotopy self-equivalences since 1988. Included also is a bibliography of some 122 articles published since 1988 and a list of problems. This book is suitable for both advanced graduate students and researchers.
This survey covers groups of homotopy self-equivalence classes of topological spaces, and the homotopy type of spaces of homotopy self-equivalences. For manifolds, the full group of equivalences and the mapping class group are compared, as are the corresponding spaces. Included are methods of calculation, numerous calculations, finite generation results, Whitehead torsion and other areas. Some 330 references are given. The book assumes familiarity with cell complexes, homology and homotopy. Graduate students and established researchers can use it for learning, for reference, and to determine the current state of knowledge.
This volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009. This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology. In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote cross-fertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.
Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.
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.
The Second Silivri Workshop functioned as a short summer school and a working conference, producing lecture notes and research papers on recent developments of Stochastic Analysis on Wiener space. The topics of the lectures concern short time asymptotic problems and anticipative stochastic differential equations. Research papers are mostly extensions and applications of the techniques of anticipative stochastic calculus.
This volume contains the proceedings of the Alpine Algebraic and Applied Topology Conference, held from August 15–21, 2016, in Saas-Almagell, Switzerland. The papers cover a broad range of topics in modern algebraic topology, including the theory of highly structured ring spectra, infinity-categories and Segal spaces, equivariant homotopy theory, algebraic -theory and topological cyclic, periodic, or Hochschild homology, intersection cohomology, and symplectic topology.
These proceedings reflect the main activities of the Paris Séminaire d'Algèbre 1989-1990, with a series of papers in Invariant Theory, Representation Theory and Combinatorics. It contains original works from J. Dixmier, F. Dumas, D. Krob, P. Pragacz and B.J. Schmid, as well as a new presentation of Derived Categories by J.E. Björk and as introduction to the deformation theory of Lie equations by J.F. Pommaret. J. Dixmier: Sur les invariants du groupe symétrique dans certaines représentations II.- B.J. Schmid: Finite groups and invariant theory.- J.E. Björk: Derived categories.- P. Pragacz: Algebro-Geometric applications of Schur S- and Q-polynomials.- F. Dumas: Sous-corps de fractions rationnelles des corps gauches de séries de Laurent.- D. Krob: Expressions rationnelles sur un anneau.- J.F. Pommaret: Deformation theory of algebraic and Geometric structures.- M. van den Bergh: Differential operators on semi-invariants for tori and weighted projective spaces.
This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homotopy pushouts and pullbacks; classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; homotopy Sets; homotopy and homology decompositions of spaces and maps; and obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. The book can be used as a text for the second semester of an advanced ungraduate or graduate algebraic topology course.
