Bundles of spectra and algebraic K-theory

Lind, J.

doi:10.2140/pjm.2016.285.427

Cited by 6 publications

(15 citation statements)

References 17 publications

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“…This makes it difficult to use the standard machinery to study algebras and modules in this category. These problems have received significant attention in the setting of parametrized stable homotopy theory [62,52,53].…”

Section: ∞-Operadsmentioning

confidence: 99%

E n -spectra and Dyer-Lashof operations

Lawson¹

2020

Handbook of Homotopy Theory

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Cohomology operations are absolutely essential in making cohomology an effective tool for studying spaces. In particular, the mod-p cohomology groups of a space X are enhanced with a binary cup product, a Bockstein derivation, and Steenrod's reduced power operations; these satisfy relations such as graded-commutativity, the Cartan formula, the Adem relations, and the instability relations [92]. The combined structure of these cohomology operations is very effective in homotopy theory because of three critical properties.These operations are natural. We can exclude the possibility of certain maps between spaces because they would not respect these operations.These operations are constrained. We can exclude the existence of certain spaces because the cup product and power operations would be incompatible with the relations that must hold. AcknowledgementsThe author would like to thank for discussions related to this material, and Haynes Miller for a careful reading of an earlier draft of this paper. The author also owes a significant long-term debt to Charles Rezk for what understanding he possesses.

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Section: ∞-Operadsmentioning

confidence: 99%

E n -spectra and Dyer-Lashof operations

Lawson¹

2020

Handbook of Homotopy Theory

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“…(See for example [27]). To understand the gauge symmetry on the manifold string topology spectrum S • P k (S 4 ) we therefore want to describe the representation…”

Section: Gauge Symmetrymentioning

confidence: 99%

“…Finally, notice that given any compact ring spectrum R, the group of units GL 1 (R) acts on its Spanier-Whitehead dual R ∨ by the dual action of GL 1 (R) on R. Given the Spanier-Whitehead duality between the manifold string topology spectrum S • P k (S 4 ) ≃ (P Ad k ) −T S 4 and the Lie group string topology spectrum S P k • (S 4 ) ≃ (P Ad k ) −Tvert then (27) describes the action of the based gauge group G b (P k ) on the Lie group string topology spectrum as well.…”

Section: Gauge Symmetrymentioning

confidence: 99%

Twisted Calabi–Yau ring spectra, string topology, and gauge symmetry

Cohen

Klang

2020

Tunisian J. Math.

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In this paper we import the theory of "Calabi-Yau" algebras and categories from symplectic topology and topological field theories, to the setting of spectra in stable homotopy theory.Twistings in this theory will be particularly important. There will be two types of Calabi-Yau structures in the setting of ring spectra: one that applies to compact algebras and one that applies to smooth algebras. The main application of twisted compact Calabi-Yau ring spectra that we will study is to describe, prove, and explain a certain duality phenomenon in string topology. This is a duality between the manifold string topology of Chas and Sullivan [8] and the Lie group string topology of Chataur-Menichi [10]. This will extend and generalize work of Gruher [20]. Then, generalizing work of the first author and Jones in [14], we show how the gauge group of the principal bundle acts on this compact Calabi-Yau structure, and we compute some explicit examples. We then extend the notion of the Calabi-Yau structure to smooth ring spectra, and prove that Thom ring spectra of (virtual) bundles over the loop space, ΩM , have this structure. In the case when M is a sphere we will use these twisted smooth Calabi-Yau ring spectra to study Lagrangian immersions of the sphere into its cotangent bundle. We recast the work of Abouzaid and Kragh [1] to show that the topological Hochschild homology of the Thom ring spectrum induced by the h-principle classifying map of the Lagrangian immersion, detects whether that immersion can be Lagrangian isotopic to an embedding. We then compute some examples. Finally, we interpret these Calabi-Yau structures directly in terms of topological Hochschild homology and cohomology.

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“…With a rate of more than 10 000 spectra per night the pipeline needs to not only provide a robust analysis, but must also be quick and have a reliable performance. Our team has extensive experience in the analysis of stellar spectra in past and ongoing spectroscopic surveys (e.g., Gaia-ESO, RAVE and GALAH) as well as in-depth knowledge about the analysis of stellar spectra including 3D stellar model atmospheres and non-LTE analysis of spectra (Bergemann et al 2012, Lind et al 2012). Currently we are benchmarking various methods (including both physical modelling of stellar spectra as well as data-driven approaches) and working on how to best implement the results from 3D modelling of stellar atmospheres and our better understanding of deviations from LTE in our analysis.…”

Section: Analysis Of Stellar Spectramentioning

confidence: 99%

Galactic Archeology with 4MOST

et al. 2017

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4MOST is a new wide-field, high-multiplex spectroscopic survey facility for the VISTA telescope of ESO. Starting in 2022, 4MOST will deploy more than 2400 fibres in a 4.1 square degree field-of-view using a positioner based on the tilting spine principle. In this contribution we give an outline of the major science goals we wish to achieve with 4MOST in the area of Galactic Archeology. The 4MOST Galactic Archeology surveys have been designed to address long-standing and far-reaching problems in Galactic science. They are focused on four major themes: 1) Near-field cosmology tests, 2) Chemo-dynamical characterisation of the major Milky Way stellar components, 3) The Galactic Halo and beyond, and 4) Discovery and characterisation of extremely metal-poor stars.In addition to a top-level description of the Galactic surveys we provide information about how the community will be able to join 4MOST via a call for Public Spectroscopic Surveys that ESO will launch.

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Bundles of spectra and algebraic K-theory

Cited by 6 publications

References 17 publications

E n -spectra and Dyer-Lashof operations

E n -spectra and Dyer-Lashof operations

Twisted Calabi–Yau ring spectra, string topology, and gauge symmetry

Galactic Archeology with 4MOST

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