Quadratic K-Theory and Geometric Topology

Williams, Byron K.

doi:10.1007/978-3-540-27855-9_13

Cited by 18 publications

(18 citation statements)

References 65 publications

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“…This is strongly supported by the recent observations of M87, which showed that the basis of the jet is very near to the ergosphere size [10,16]. Other evidences include a quasiperfect collimation [5] along z with big energies [6], the possibility of a Penrose process [2,3,9], and/or a BSW effect [17]. Besides, this repulsive force can also be the source of cosmic rays of high energy, specially of neutrinos.…”

Section: Discussionsupporting

confidence: 53%

“…In this paper, we study timelike geodesics of the Kerr space-time that follow its axis of symmetry. These geodesics revealed great importance to build a possible mechanism to explain the production of very high energy particles and of extragalactic jets stemming from the centre of galaxies [1][2][3][4][5][6][7][8]. It is widely accepted that the centre of galaxies encloses a Kerr black hole and particles, from the accretion disk, can fall into it by crossing the ergosphere.…”

Section: Introductionmentioning

confidence: 99%

“…It is widely accepted that the centre of galaxies encloses a Kerr black hole and particles, from the accretion disk, can fall into it by crossing the ergosphere. Inside the ergosphere they may undergo a Penrose process producing new particles that can be ejected with high energies [2,3,9]. These particles can follow collimated geodesics near the axis of symmetry of the black hole, and thus form the extragalactic jets.…”

Section: Introductionmentioning

confidence: 99%

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Kerr geodesics following the axis of symmetry

2016

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We present here the general expressions for the acceleration of massive test particles along the symmetry axis of the Kerr metric, and then study the main properties of this acceleration in different regions of the spacetime. In particular, we show that there exists a region near the black hole in which the gravitational field is repulsive. We provide possible physical interpretations about the role of this effect in terms of the different conserved parameters. The studies of these geodesics are important not only to understand better the structure of the Kerr spacetime but also to its use as a possible mechanism for the production of extragalactic jets. Our results are obtained with the help of expressing the geodesics of the Kerr spacetime in terms of the Weyl coordinates.

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Section: Discussionsupporting

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kerr geodesics following the axis of symmetry

2016

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“…On the other hand, as a consequence of the fundamental theorem of hermitian K-theory (cf. [5] p. 264), we have an isomorphism of L * -modules between ε L n ( U A r ) and ε L n ( U A r+4 ) (as noticed also by Williams [9]). Therefore, the previous direct limit is simply the limit of the system…”

Section: Theoremsupporting

confidence: 62%

Stabilization of the Witt group

Karoubi

2006

Comptes Rendus. Mathématique

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Abstract.In this Note, using an idea due to Thomason [8], we define a "homology theory" on the category of rings which satisfies excision, exactness, homotopy (in the algebraic sense) and periodicity of order 4. For regular noetherian rings, we find Balmers's higher Witt groups. For more general rings, this homology is isomorphic to the KT-theory of Hornbostel [3], inspired by the work of Williams [9]. For real or complex C*-algebras, we recover -up to 2 torsion -topological K-theory.

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“…This construction provides many counterexamples to a conjecture of B. Williams [50]. More specifically, we have for instance the following theorem.…”

Section: A Ring With Trivial K-theory and Nontrivial Kq-theorymentioning

confidence: 86%

Hermitian K-theory and 2-regularity for totally real number fields

2010

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We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. Moreover, the 2-regular case is precisely the class of totally real number fields that have homotopy cartesian "Bökstedt square", relating the K-theory of the 2-integers to that of the fields of real and complex numbers and finite fields. We also identify the homotopy fibers of the forgetful and hyperbolic maps relating hermitian and algebraic K-theory. The result is then exactly periodic of period 8 in the orthogonal case. In both the orthogonal and symplectic cases, we prove a 2-primary hermitian homotopy limit conjecture for these rings.

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Quadratic K-Theory and Geometric Topology

Cited by 18 publications

References 65 publications

Kerr geodesics following the axis of symmetry

Kerr geodesics following the axis of symmetry

Stabilization of the Witt group

Hermitian K-theory and 2-regularity for totally real number fields

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