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"H-spaces"
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Architects of an American landscape : Henry Hobson Richardson, Frederick Law Olmsted, and the reimagining of America's public and private spaces
\"As the nation recovered from a cataclysmic war, two titans of design profoundly influenced how Americans came to interact with the built and natural world around them through their pioneering work in architecture and landscape design. Frederick Law Olmsted is widely revered as America's first and finest parkmaker and environmentalist, the force behind Manhattan's Central Park, Brooklyn's Prospect Park, Biltmore's parkland in Asheville, dozens of parks across the country, and the preservation of Yosemite and Niagara Falls. Yet his close friend and sometime collaborator, Henry Hobson Richardson, has been almost entirely forgotten today, despite his outsized influence on American architecture-from Boston's iconic Trinity Church to Chicago's Marshall Field Wholesale Store to the Shingle Style and the wildly popular \"open plan\" he conceived for family homes. Individually they created much-beloved buildings and public spaces. Together they married natural landscapes with built structures in train stations and public libraries that helped drive the shift in American life from congested cities to developing suburbs across the country. The small, reserved Olmsted and the passionate, Falstaffian Richardson could not have been more different in character, but their sensibilities were closely aligned. In chronicling their intersecting lives and work in the context of the nation's post-war renewal, Hugh Howard reveals how these two men created original all-American idioms in architecture and landscape that influence how we enjoy our public and private spaces to this day\"-- Provided by publisher.
BOOK
The Euler characteristic of a transitive Lie algebroid
We apply the Atiyah–Singer index theorem and tensor products of elliptic complexes to the cohomology of transitive Lie algebroids. We prove that the Euler characteristic of a representation of a transitive Lie algebroid A over a compact manifold M vanishes unless A=TM , and prove a general Künneth formula. As applications, we give a short proof of a vanishing result for the Euler characteristic of a principal bundle calculated using invariant differential forms, and show that the cohomology of certain Lie algebroids are exterior algebras. The latter result can be seen as a generalization of Hopf's theorem regarding the cohomology of compact Lie groups.
Journal Article
Erdîos space and homeomorphism groups of manifolds
Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group \\mathcal{H}(M,D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. The authors present a complete solution to the topological classification problem for \\mathcal{H}(M,D) as follows. If M is a one-dimensional topological manifold, then they proved in an earlier paper that \\mathcal{H}(M,D) is homeomorphic to \\mathbb{Q}^\\omega, the countable power of the space of rational numbers. In all other cases they find in this paper that \\mathcal{H}(M,D) is homeomorphic to the famed Erdős space \\mathfrak E, which consists of the vectors in Hilbert space \\ell^2 with rational coordinates. They obtain the second result by developing topological characterizations of Erdős space.
eBook
Comultiplication Structures for aWedge of Spheres
In this paper, we consider the various sets of comultiplications of a wedge of spheres and provide some methods to calculate many kinds of comultiplications with different properties. In particular, we concentrate on studying to compute the number of comultiplications, associative comultiplications, commutative comultiplications, and comultiplications which are both associative and commutative of a wedge of spheres. The more spheres that appear in a wedge, the more complicate the proofs and computations become. Our methods involve the basic Whitehead products in a wedge of spheres and the Hopf-Hilton invariants.
Journal Article
Generalized convexity and applications to fixed points and equilibria
In this paper, we give a uniform approach for generalized convexity by using the concept of L-convexity defined by Ben El-Mechaiekh et al. (J Math Anal Appl 222:138–150, 1998). We prove that the generalized notion of L-space contains well-known generalized convex spaces defined in the literature in topological vector spaces as well as several generalized convexity structures defined on metric spaces. In this context, we give a generalized version of the Fan–Knaster–Kuratowski–Mazurkiewicz Principle (FKKM Principle) in L-spaces and a Browder-Fan type theorem about the existence of fixed points for open lower section set-valued maps defined in an L-space. As an application, we prove the existence of equilibria for an abstract economy with an infinite number of agents.
Journal Article
Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type
For a finite group G of Lie type and a prime p, the authors compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from \\mathrm{Out}(G) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of BG^\\wedge _p in terms of \\mathrm{Out}(G).
eBook
Abelian Properties of Anick Spaces
Anick spaces are closely connected with both EHP sequences and the study of torsion exponents. In addition they refine the secondary
suspension and enter unstable periodicity. In this work we describe their
eBook
