Results 11 to 20 of about 2,551 (80)
Levels of algebraicity in stable homotopy theories
Journal of the London Mathematical Society, Volume 108, Issue 2, Page 545-577, August 2023., 2023 Abstract We study several different notions of algebraicity in use in stable homotopy theory and prove implications between them. The relationships between the different meanings of algebraic are unexpectedly subtle, and we illustrate this with several interesting examples arising from chromatic homotopy theory.
Jocelyne Ishak +2 more
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Journal of Topology, Volume 15, Issue 3, Page 1325-1454, September 2022., 2022 Abstract We introduce a global equivariant refinement of algebraic K‐theory; here ‘global equivariant’ refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global Ω$\Omega$‐spectrum that keeps track of genuine G$G$‐equivariant infinite loop spaces, for all finite ...
Stefan Schwede
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Eilenberg Mac Lane spectra as p$p$‐cyclonic Thom spectra
Journal of Topology, Volume 15, Issue 2, Page 878-895, June 2022., 2022 Abstract Hopkins and Mahowald gave a simple description of the mod p$p$ Eilenberg Mac Lane spectrum Fp${\mathbb {F}}_p$ as the free E2$\mathbb {E}_2$‐algebra with an equivalence of p$p$ and 0. We show for each faithful 2‐dimensional representation λ$\lambda$ of a p$p$‐group G$G$ that the G$G$‐equivariant Eilenberg Mac Lane spectrum F̲p$\underline ...
Ishan Levy
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On the homotopy type of L‐spectra of the integers
Journal of Topology, Volume 14, Issue 1, Page 183-214, March 2021., 2021 Abstract We show that quadratic and symmetric L‐theory of the integers are related by Anderson duality and that both spectra split integrally into the L‐theory of the real numbers and a generalised Eilenberg–Mac Lane spectrum. As a consequence, we obtain a corresponding splitting of the space G/Top. Finally, we prove analogous results for the genuine L‐
Fabian Hebestreit +2 more
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Some torsion classes in the Chow ring and cohomology of BPGLn
Journal of the London Mathematical Society, Volume 103, Issue 1, Page 127-160, January 2021., 2021 Abstract In the integral cohomology ring of the classifying space of the projective linear group PGLn (over C), we find a collection of p‐torsion classes yp,k of degree 2(pk+1+1) for any odd prime divisor p of n, and k⩾0. If, in addition, p2∤n, there are p‐torsion classes ρp,k of degree pk+1+1 in the Chow ring of the classifying stack of PGLn, such ...
Xing Gu
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Journal of Topology, Volume 13, Issue 3, Page 939-968, September 2020., 2020 Abstract We specify exterior generators in π∗THH(MU)=π∗(MU)⊗E(λn′∣n⩾1) and π∗THH(BP)=π∗(BP)⊗E(λn∣n⩾1), and calculate the action of the σ‐operator on these graded rings. In particular, σ(λn′)=0 and σ(λn)=0, while the actions on π∗(MU) and π∗(BP) are expressed in terms of the right units ηR in the Hopf algebroids (π∗(MU),π∗(MU∧MU)) and (π∗(BP),π∗(BP∧BP)),
John Rognes
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Framed transfers and motivic fundamental classes
Journal of Topology, Volume 13, Issue 2, Page 460-500, June 2020., 2020 Abstract We relate the recognition principle for infinite P1‐loop spaces to the theory of motivic fundamental classes of Déglise, Jin and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories represented by motivic spectra: the framed transfers given by the recognition principle, which arise from Voevodsky's ...
Elden Elmanto +4 more
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Sectional Category of the Ganea Fibrations and Higher Relative Category
Chinese Journal of Mathematics, Volume 2016, Issue 1, 2016., 2016 We first compute James’ sectional category (secat) of the Ganea map gk of any map ιX in terms of the sectional category of ιX: we show that secat gk is the integer part of secat ιX/(k + 1). Next we compute the relative category (relcat) of gk. In order to do this, we introduce the relative category of order k (relcatk) of a map and show that relcat gk ...
Jean-Paul Doeraene, Dan Burghelea
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Vector bundles over three‐dimensional spherical space forms
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We consider the problem of enumerating the G‐bundles over low‐dimensional manifolds (dimension ≤3) and in particular vector bundles over the three‐dimensional spherical space forms. We give a complete answer to these questions and we give tables for the possible vector bundles over the 3‐dimensional spherical space forms.
Esdras Teixeira Costa +2 more
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Transfers for ramified covering maps in homology and cohomology
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 Making use of a modified version, due to McCord, of the Dold‐Thom construction of ordinary homology, we give a simple topological definition of a transfer for ramified covering maps in homology with arbitrary coefficients. The transfer is induced by a suitable map between topological groups. We also define a new cohomology transfer which is dual to the
Marcelo A. Aguilar, Carlos Prieto
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