Introduction

Baum, Siegmund J.

doi:10.1007/978-1-4612-3762-4_1

Cited by 3 publications

(4 citation statements)

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“…(resp., H n .W; @W s £ .w/Z/). Moreover, F restricts to f on N , and F restricts 3 to an infinitesimally controlled homotopy equivalence F j @ 2 V @ 2 V 3 @ 2 W over X:…”

Section: A New Definition Of the Structure Groupmentioning

confidence: 99%

“…This makes the definition of S n .X; w/ functorial. 3 Here we are using an obvious generalization of Definition 3.3 to the case of manifold 2-ads or manifold n-ads. 4 For example, for the element h .M; @M; '; N; @N; ; f / P S.X; w/, induces a canonical local coefficient isomorphism ' £ .w/ 3 .…”

Section: A New Definition Of the Structure Groupmentioning

confidence: 99%

“…where the notation 1 2 means Z 1 2 , R and are Baum-Connes assembly maps [3,4], and 1 and 2 are induced by changing the scalars from R to C. In particular, if we assume the split injectivity of the Baum-Connes assembly map, then we also have the Novikov rho invariant map in the real case:…”

Section: Novikov Rho Invariant and Strong Novikov Conjecturementioning

confidence: 99%

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Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds

Weinberger

Xie

2020

Comm Pure Appl Math

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Let X be a closed oriented connected topological manifold of dimension n ! 5. The structure group S TOP .X/ is the abelian group of equivalence classes of all pairs .f; M / such that M is a closed oriented manifold and f M 3 X is an orientation-preserving homotopy equivalence. The main purpose of this article is to prove that a higher rho invariant map defines a group homomorphism from the topological structure group S TOP .X/ of X to the analytic structure group K n .C £ L;0. z X/ / of X. Here z X is the universal cover of X, h 1 X is the fundamental group of X, and C £ L;0. z X/ is a certain C £-algebra. In fact, we introduce a higher rho invariant map on the homology manifold structure group of a closed oriented connected topological manifold, and prove its additivity. This higher rho invariant map restricts to the higher rho invariant map on the topological structure group. More generally, the same techniques developed in this paper can be applied to define a higher rho invariant map on the homology manifold structure group of a closed oriented connected homology manifold. As an application, we use the additivity of the higher rho invariant map to study nonrigidity of topological manifolds. More precisely, we give a lower bound for the free rank of the algebraically reduced structure group of X by the number of torsion elements in 1 X. Here the algebraically reduced structure group of X is the quotient of S TOP .X/ modulo a certain action of self-homotopy equivalences of X. We also introduce a notion of homological higher rho invariant, which can be used to detect many elements in the structure group of a closed oriented topological manifold, even when the fundamental group of the manifold is torsion free. In particular, we apply this homological higher rho invariant to show that the structure group is not finitely generated for a class of manifolds.

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“…(resp., H n .W; @W s £ .w/Z/). Moreover, F restricts to f on N , and F restricts 3 to an infinitesimally controlled homotopy equivalence F j @ 2 V @ 2 V 3 @ 2 W over X:…”

Section: A New Definition Of the Structure Groupmentioning

confidence: 99%

Section: A New Definition Of the Structure Groupmentioning

confidence: 99%

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Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds

Weinberger

Xie

2020

Comm Pure Appl Math

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“…ISEH was established in 1950 by hematologists around the world to accelerate the search for remedies to address the enormous clinical needs raised by the aftermath of the atomic bombings of Hiroshima and Nagasaki. All the scientific players of the EPO saga were prominent figures of this society; for example, Dr. Takaku co-edited a book dedicated to advances in bone marrow transplantation sponsored by the Society [49]; Dr. Dukes became treasurer of ISEH in 1972 and covered this position for over 20 years, and John was a devoted member of the Society and was elected as President in 1993. These investigators had the opportunity to discuss the various facets of EPO during the annual meetings of the Society.…”

Section: Epo Becomes a Worldwide Pharmaceutical Businessmentioning

confidence: 99%

Erythropoietin: A Personal Alice in Wonderland Trip in the Shadow of the Giants

Migliaccio

2024

Biomolecules

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The identification of the hormone erythropoietin (EPO), which regulates red blood cell production, and its development into a pharmaceutical-grade product to treat anemia has been not only a herculean task but it has also been the first of its kind. As with all the successes, it had “winners” and “losers”, but its history is mostly told by the winners who, over the years, have published excellent scientific and divulgate summaries on the subject, some of which are cited in this review. In addition, “success” is also due to the superb and dedicated work of numerous “crew” members, who often are under-represented and under-recognized when the story is told and often have several “dark sides” that are not told in the polished context of most reviews, but which raised the need for the development of the current legislation on biotherapeutics. Although I was marginally involved in the clinical development of erythropoietin, I have known on a personal basis most, if not all, the protagonists of the saga and had multiple opportunities to talk with them on the drive that supported their activities. Here, I will summarize the major steps in the development of erythropoietin as the first bioproduct to enter the clinic. Some of the “dark sides” will also be mentioned to emphasize what a beautiful achievement of humankind this process has been and how the various unforeseen challenges that emerged were progressively addressed in the interest of science and of the patient’s wellbeing.

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Isomorphism conjectures in algebraic 𝐾-theory

Farrell¹,

Jones²

1993

J. Amer. Math. Soc.

103

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In this paper we are concerned with the four functors .9*, .9: iff , ~ , and £:-00 , which map from the category of topological spaces X to the category d'ff of n-spectra. The functor .9* ( ) (or .9* 1 ( )) maps the space X to the nspectrum of stable topological (or smooth) pseudoisotopies of X. (The spaces .9 i (X) , .9 i diff (X) , i ;::: 0, are Hatcher's deloopings of .9 0 (X) , .9~iff(X) (cf.[29])). The functor ~() maps a path-connected space X to the algebraic Ktheoretic n-spectrum for the integral group ring Z1l, X. (The spaces ~ (X) , i ;::: 0, are the Gersten-Wagoner deloopings of ~(X); cf. [27,52].) ~(X) is also defined on a nonpath-connected space X to be EBiEI~(Xi)' where {Xi: i E /} are the path components of X and EB iEI ~ (Xi) indicates the direct limit of all finite products of the {~(Xi): i E I}. If X is path connected then the functor £:-00 () maps X to the L -00 -surgery classifying spaces for oriented surgery problems with fundamental group 1l, X identified by their fourfold periodicity ~-OO(X) = ~~~(X) (cf. [35,39,44,47]). In addition, if X is not path connected then we set £:-OO(X) = EBiE1£:-00(X i ) , where {Xi: i E i} are the path components of X.

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Introduction

Cited by 3 publications

References 2 publications

Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds

Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds

Erythropoietin: A Personal Alice in Wonderland Trip in the Shadow of the Giants

Isomorphism conjectures in algebraic 𝐾-theory

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