The Goodwillie Tower And The Ehp Sequence

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The Goodwillie Tower And The Ehp Sequence

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Author : Mark Behrens
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

The Goodwillie Tower And The Ehp Sequence written by Mark Behrens and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

The author studies the interaction between the EHP sequence and the Goodwillie tower of the identity evaluated at spheres at the prime $2$. Both give rise to spectral sequences (the EHP spectral sequence and the Goodwillie spectral sequence, respectively) which compute the unstable homotopy groups of spheres. He relates the Goodwillie filtration to the $P$ map, and the Goodwillie differentials to the $H$ map. Furthermore, he studies an iterated Atiyah-Hirzebruch spectral sequence approach to the homotopy of the layers of the Goodwillie tower of the identity on spheres. He shows that differentials in these spectral sequences give rise to differentials in the EHP spectral sequence. He uses his theory to recompute the $2$-primary unstable stems through the Toda range (up to the $19$-stem). He also studies the homological behavior of the interaction between the EHP sequence and the Goodwillie tower of the identity. This homological analysis involves the introduction of Dyer-Lashof-like operations associated to M. Ching's operad structure on the derivatives of the identity. These operations act on the mod $2$ stable homology of the Goodwillie layers of any functor from spaces to spaces.

Issues In General And Specialized Mathematics Research 2013 Edition

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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2013-05-01

Issues In General And Specialized Mathematics Research 2013 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-01 with Mathematics categories.

Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Handbook Of Homotopy Theory

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Author : Haynes Miller
language : en
Publisher: CRC Press
Release Date : 2020-01-23

Handbook Of Homotopy Theory written by Haynes Miller and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Mathematics categories.

The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

On The Shape Of A Pure O Sequence

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Author : Mats Boij
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

On The Shape Of A Pure O Sequence written by Mats Boij and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

A monomial order ideal is a finite collection X of (monic) monomials such that, whenever M∈X and N divides M, then N∈X. Hence X is a poset, where the partial order is given by divisibility. If all, say t t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h_=(h0=1,h1,...,he), counting the monomials of X in each degree. Equivalently, pure O-sequences can be characterized as the f-vectors of pure multicomplexes, or, in the language of commutative algebra, as the h h-vectors of monomial Artinian level algebras. Pure O-sequences had their origin in one of the early works of Stanley's in this area, and have since played a significant role in at least three different disciplines: the study of simplicial complexes and their f f-vectors, the theory of level algebras, and the theory of matroids. This monograph is intended to be the first systematic study of the theory of pure O-sequences.

Finite Order Automorphisms And Real Forms Of Affine Kac Moody Algebras In The Smooth And Algebraic Category

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Author : Ernst Heintze
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Finite Order Automorphisms And Real Forms Of Affine Kac Moody Algebras In The Smooth And Algebraic Category written by Ernst Heintze and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

Heintze and Gross discuss isomorphisms between smooth loop algebras and of smooth affine Kac-Moody algebras in particular, and automorphisms of the first and second kinds of finite order. Then they consider involutions of the first and second kind, and make the algebraic case. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).

Cubical Homotopy Theory

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Author : Brian A. Munson
language : en
Publisher: Cambridge University Press
Release Date : 2015-10-06

Cubical Homotopy Theory written by Brian A. Munson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-06 with Mathematics categories.

A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.

The Kohn Sham Equation For Deformed Crystals

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Author : Weinan E
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-01-25

The Kohn Sham Equation For Deformed Crystals written by Weinan E and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-25 with Mathematics categories.

The solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, the authors also establish a number of fundamental properties of the Kohn-Sham map.

Characterization And Topological Rigidity Of Nobeling Manifolds

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Author : Andrzej Nagórko
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-22

Characterization And Topological Rigidity Of Nobeling Manifolds written by Andrzej Nagórko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.

The author develops a theory of Nobeling manifolds similar to the theory of Hilbert space manifolds. He shows that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular the author proves the Nobeling manifold characterization conjecture.

Potential Wadge Classes

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Author : Dominique Lecomte
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-01-25

Potential Wadge Classes written by Dominique Lecomte and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-25 with Mathematics categories.

Let $\bf\Gamma$ be a Borel class, or a Wadge class of Borel sets, and $2\!\leq\! d\!\leq\!\omega$ be a cardinal. A Borel subset $B$ of ${\mathbb R}^d$ is potentially in $\bf\Gamma$ if there is a finer Polish topology on $\mathbb R$ such that $B$ is in $\bf\Gamma$ when ${\mathbb R}^d$ is equipped with the new product topology. The author provides a way to recognize the sets potentially in $\bf\Gamma$ and applies this to the classes of graphs (oriented or not), quasi-orders and partial orders.

Pseudo Differential Operators With Discontinuous Symbols Widom S Conjecture

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Author : Aleksandr Vladimirovich Sobolev
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-26

Pseudo Differential Operators With Discontinuous Symbols Widom S Conjecture written by Aleksandr Vladimirovich Sobolev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-26 with Mathematics categories.

Relying on the known two-term quasiclassical asymptotic formula for the trace of the function $f(A)$ of a Wiener-Hopf type operator $A$ in dimension one, in 1982 H. Widom conjectured a multi-dimensional generalization of that formula for a pseudo-differential operator $A$ with a symbol $a(\mathbf{x}, \boldsymbol{\xi})$ having jump discontinuities in both variables. In 1990 he proved the conjecture for the special case when the jump in any of the two variables occurs on a hyperplane. The present paper provides a proof of Widom's Conjecture under the assumption that the symbol has jumps in both variables on arbitrary smooth bounded surfaces.