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Showing 1 to 10 of 10 for “"stable homotopy"”.
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Twisted stable homotopy theory
… are two natural interpretations of a twist of stable homotopy theory. The first interpretation of a twist is as a nontrivial bundle whose fibre is the stable homotopy category. This kind of radical global twist forms the basis for twisted parametrized stable homotopy theory, which is introduced …
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Spectral Fukaya Categories for Liouville Manifolds
This thesis constructs stable homotopy types underlying symplectic Floer homology, realizing a program proposed by Cohen, Jones and Segal twenty-five years ago. We work in the setting of Liouville manifolds with a stable symplectic trivialization of their tangent bundles, where we prove that the …
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The algebraic K-theory of the chromatic filtration and the telescope conjecture
… coming from the chromatic filtration of the stable homotopy category, and apply these tools to improve our understanding of the large scale structure of stable homotopy theory and understand Ravenel's telescope conjecture. More specifically, in joint work with Burklund, we prove a general …
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The generalized Tate construction
… Tate construction tk reduces chromatic level in stable homotopy theory. The first parts introduce the construction and discuss chromatic reduction. The next section makes a computation and gives the duals of L(n) = L(n)1. The last part looks ahead, mentioning how this computation could be …
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Generalizations Of The Segal Conjecture
… over the Burnside ring A(G). Define a map to stable homotopy which sends this subhomomorphism to the stable map BG{dollar}sb+{dollar} {dollar}{lcub}buildrelrm transferoverlongrightarrow{rcub}{dollar} BH{dollar}sb+{dollar} {dollar}{lcub}buildrelrm Brhosb+overlongrightarrow{rcub}{dollar} …
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The v₁-periodic part of the Adams spectral sequence at an odd prime/
We tell the story of the stable homotopy groups of spheres for odd primes at chromatic height 1 through the lens of the Adams spectral sequence. We find the "dancers to a discordant system." We calculate a Bockstein spectral sequence which converges to the 1-line of the chromatic spectral sequence …
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L-functions and J-spectra
… is an important topic in chromatic homotopy theory at height 1. Both sides are related to the special values of the Riemann ζ-function. Number theorists have studied the twistings of the Riemann ζ-functions and Eisenstein series by Dirichlet characters. We first explain congruences …
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MOTIVIC HOCHSCHILD HOMOLOGY
… field k, and let SH(S) be Morel and Voevodski's stable motivic homotopy category over S. Let R be a motivic ring spectrum in SH(S); we define the motivic Hochschild homology of R via the derived tensor product: MHH(R)=R ∧_{R ∧ R^{op}} R. This spectrum can be considered the motivic analogue of …
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Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications
… We then interpret these computations of the homotopy of relative smash products as being related to obstructions to having $E_infty$ ring maps. The operations in the $C_2$-equivariant Adams spectral sequence are a partial extension of the work of Bruner in cite{HRS} and have applications to …
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Transchromatic generalized character maps
"In ""Generalized Group Characters and Complex Oriented Cohomology Theories"", Hopkins, Kuhn, and Ravenel discovered a generalized character theory that proved useful in studying cohomology rings of the form E^*(BG). In this paper we use the geometry of p-divisible groups to describe a sequence of …