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Author: Jie Wu
Publisher: American Mathematical Soc.
ISBN: 0821832395
Category : Mathematics
Languages : en
Pages : 148
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Book Description
Investigates the homotopy theory of the suspensions of the real projective plane. This book computes the homotopy groups up to certain range. It also studies the decompositions of the self smashes and the loop spaces with some applications to the Stiefel manifolds.
Author: Jie Wu
Publisher: American Mathematical Soc.
ISBN: 0821832395
Category : Mathematics
Languages : en
Pages : 148
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Book Description
Investigates the homotopy theory of the suspensions of the real projective plane. This book computes the homotopy groups up to certain range. It also studies the decompositions of the self smashes and the loop spaces with some applications to the Stiefel manifolds.
Author: Jie Wu
Publisher:
ISBN: 9780821832394
Category : Group theory
Languages : en
Pages : 130
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Book Description
Author: Douglas C. Ravenel
Publisher: Princeton University Press
ISBN: 9780691025728
Category : Mathematics
Languages : en
Pages : 228
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Book Description
Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Author: Stefano Marmi
Publisher: American Mathematical Soc.
ISBN: 0821833251
Category : Mathematics
Languages : en
Pages : 98
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Book Description
We prove that the solutions of a cohomological equation of complex dimension one and in the analytic category have a monogenic dependence on the parameter. This cohomological equation is the standard linearized conjugacy equation for germs of holomorphic maps in a neighborhood of a fixed point.
Author: Ethan Akin
Publisher: American Mathematical Soc.
ISBN: 0821833383
Category : Mathematics
Languages : en
Pages : 146
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Book Description
The goal of this work is to describe the dynamics of generic homeomorphisms of certain compact metric spaces $X$. Here ``generic'' is used in the topological sense -- a property of homeomorphisms on $X$ is generic if the set of homeomorphisms with the property contains a residual subset (in the sense of Baire category) of the space of all homeomorphisms on $X$. The spaces $X$ we consider are those with enough local homogeneity to allow certain localized perturbations of homeomorphisms; for example, any compact manifold is such a space. We show that the dynamics of a generic homeomorphism is quite complicated, with a number of distinct dynamical behaviors coexisting (some resemble subshifts of finite type, others, which we call `generalized adding machines', appear strictly periodic when viewed to any finite precision, but are not actually periodic). Such a homeomorphism has infinitely many, intricately nested attractors and repellors, and uncountably many distinct dynamically-connected components of the chain recurrent set. We single out several types of these ``chain components'', and show that each type occurs densely (in an appropriate sense) in the chain recurrent set. We also identify one type that occurs generically in the chain recurrent set. We also show that, at least for $X$ a manifold, the chain recurrent set of a generic homeomorphism is a Cantor set, so its complement is open and dense. Somewhat surprisingly, there is a residual subset of $X$ consisting of points whose limit sets are chain components of a type other than the type of chain components that are residual in the space of all chain components. In fact, for each generic homeomorphism on $X$ there is a residual subset of points of $X$ satisfying a stability condition stronger than Lyapunov stability.
Author: J. T. Cox
Publisher: American Mathematical Soc.
ISBN: 0821835424
Category : Mathematics
Languages : en
Pages : 114
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Book Description
Studies the evolution of the large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. This title introduces the concept of a continuum limit in the hierarchical mean field limit.
Author: William Norrie Everitt
Publisher: American Mathematical Soc.
ISBN: 0821835459
Category : Mathematics
Languages : en
Pages : 94
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Book Description
Complex symplectic spaces are non-trivial generalizations of the real symplectic spaces of classical analytical dynamics. This title presents a self-contained investigation of general complex symplectic spaces, and their Lagrangian subspaces, regardless of the finite or infinite dimensionality.
Author: Marcin Bownik
Publisher: American Mathematical Soc.
ISBN: 082183326X
Category : Mathematics
Languages : en
Pages : 136
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Book Description
Investigates the anisotropic Hardy spaces associated with very general discrete groups of dilations. This book includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon and Torchinsky.
Author: Ottmar Loos
Publisher: American Mathematical Soc.
ISBN: 0821835467
Category : Mathematics
Languages : en
Pages : 232
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Book Description
We develop the basic theory of root systems $R$ in a real vector space $X$ which are defined in analogy to the usual finite root systems, except that finiteness is replaced by local finiteness: the intersection of $R$ with every finite-dimensional subspace of $X$ is finite. The main topics are Weyl groups, parabolic subsets and positive systems, weights, and gradings.
Author: Masaaki Furusawa
Publisher: American Mathematical Soc.
ISBN: 0821833286
Category : Mathematics
Languages : en
Pages : 158
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Book Description
Proves two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, the group of $4$ by $4$ symplectic similitude matrices. This book conjectures that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $\mathrm{g1}\left(2\right)$ in [{J1}] and [{J2}].
