Iterating The Cobar Construction
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| Author | : Justin R. Smith |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 154 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 0821825887 |
This paper develops a new invariant of a CW-complex called the m-structure and uses it to perform homotopy-theoretic computations. The m-structure of a space encapsulates the coproduct structure, as well as higher-coproduct structures that determine Steenrod-operations. Given an m-structure on the chain complex of a reduced simplicial complex of a pointed simply-connected space, one can equip the cobar construction of this chain-complex with a natural m-structure. This result allows one to form iterated cobar constructions that are shown to be homotopy equivalent to iterated loop-spaces.
| Author | : Hans J. Baues |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 194 |
| Release | : 1980 |
| Genre | : Mathematics |
| ISBN | : 0821822306 |
The homology of iterated loop spaces [capital Greek]Omega [superscript]n [italic]X has always been a problem of major interest because it gives some insight into the homotopy of [italic]X, among other things. Therefore, if [italic]X is a CW-complex, one has been interested in small CW models for [capital Greek]Omega [superscript]n [italic]X in order to compute the cellular chain complex. The author proves a very general model theorem from which he can derive models, in addition to very technical proofs of the model theorem for several other models.
| Author | : Roger D. Nussbaum |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 148 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : 0821824546 |
| Author | : Francois Sigrist |
| Publisher | : Springer |
| Total Pages | : 165 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540366210 |
| Author | : Martin Markl |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821843621 |
Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.
| Author | : John McCleary |
| Publisher | : Cambridge University Press |
| Total Pages | : 579 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0521567599 |
Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.
| Author | : I.M. James |
| Publisher | : Elsevier |
| Total Pages | : 1336 |
| Release | : 1995-07-18 |
| Genre | : Mathematics |
| ISBN | : 0080532985 |
Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.
| Author | : Mauro Beltrametti |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 79 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821802348 |
This work studies the adjunction theory of smooth 3-folds in P]5. Because of the many special restrictions on such 3-folds, the structure of the adjunction theoretic reductions are especially simple, e.g. the 3-fold equals its first reduction, the second reduction is smooth except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given 3-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such 3-folds up to degree 12 are included. Many of the general results are shown to hold for smooth projective n-folds embedded in P]N with N 2n -1.
| Author | : Masakazu Nasu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 230 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821826069 |
We introduce the notion of a textile system. Using this, we study the dynamical properties of endomorphisms and automorphisms of topological Markov shifts including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied.
| Author | : Ran Levi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 121 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821804014 |
In part 1 we study the homology, homotopy, and stable homotopy of [capital Greek]Omega[italic capital]B[lowercase Greek]Pi[up arrowhead][over][subscript italic]p, where [italic capital]G is a finite [italic]p-perfect group. In part 2 we define the concept of resolutions by fibrations over an arbitrary family of spaces.
