Virtual vector bundles and graded Thom spectra
نویسندگان
چکیده
منابع مشابه
Units of Ring Spectra and Thom Spectra
We review and extend the theory of Thom spectra and the associated obstruction theory for orientations. Specifically, we show that for an E∞ ring spectrum A, the classical construction of gl1A, the spectrum of units, is the right adjoint of the functor Σ∞+ Ω ∞ : ho(connective spectra) → ho(E∞ ring spectra). To a map of spectra f : b → bgl1A, we associate an E∞ A-algebra Thom spectrum Mf , which...
متن کاملBetti Numbers of Graded Modules and Cohomology of Vector Bundles
In a remarkable paper Mats Boij and Jonas Söderberg [2006] conjectured that the Betti table of a Cohen-Macaulay module over a polynomial ring is a positive linear combination of Betti tables of modules with pure resolutions. We prove a strengthened form of their Conjectures. Applications include a proof of the Multiplicity Conjecture of Huneke and Srinivasan and a proof of the convexity of a fa...
متن کاملPolarisation of Graded Bundles
We construct the full linearisation functor which takes a graded bundle of degree k (a particular kind of graded manifold) and produces a k-fold vector bundle. We fully characterise the image of the full linearisation functor and show that we obtain a subcategory of k-fold vector bundles consisting of symmetric k-fold vector bundles equipped with a family of morphisms indexed by the symmetric g...
متن کاملRing Spectra Which Are Thom Complexes
commutes up to homotopy where T is the map that exchanges factors. Let L be a space and let be a fibration over L classified by a mapf L BF (the classifying space of stable spherical fibrations). We can form the Thom spectrum T(f) of f as a suspension spectrum by letting (T(f)) be the Thorn complex of L n--YBFn where L is the n-skeleton of L. This makes T(f)-{(T(f))n) into a suspension spectrum...
متن کاملLocally trivial quantum vector bundles and associated vector bundles
We define locally trivial quantum vector bundles (QVB) and construct such QVB associated to locally trivial quantum principal fibre bundles. The construction is quite analogous to the classical construction of associated bundles. A covering of such bundles is induced from the covering of the subalgebra of coinvariant elements of the principal bundle. There exists a differential structure on the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2018
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-018-2131-0