4,201 research outputs found
Brane structures in microlocal sheaf theory
Let be an exact Lagrangian submanifold of a cotangent bundle ,
asymptotic to a Legendrian submanifold . We study
a locally constant sheaf of -categories on , called the sheaf of
brane structures or . Its fiber is the -category of
spectra, and we construct a Hamiltonian invariant, fully faithful functor from
to the -category of sheaves of spectra on
with singular support in .Comment: 35 pages, 13 figure
Stratifying derived categories of cochains on certain spaces
In recent years, Benson, Iyengar and Krause have developed a theory of
stratification for compactly generated triangulated categories with an action
of a graded commutative Noetherian ring. Stratification implies a
classification of localizing and thick subcategories in terms of subsets of the
prime ideal spectrum of the given ring. In this paper two stratification
results are presented: one for the derived category of a commutative
ring-spectrum with polynomial homotopy and another for the derived category of
cochains on certain spaces. We also give the stratification of cochains on a
space a topological content.Comment: 27 page
Stratification and duality for homotopical groups
We generalize Quillen's -isomorphism theorem, Quillen's stratification
theorem, the stable transfer, and the finite generation of cohomology rings
from finite groups to homotopical groups. As a consequence, we show that the
category of module spectra over is stratified
and costratified for a large class of -local compact groups
including compact Lie groups, connected -compact groups, and -local
finite groups, thereby giving a support-theoretic classification of all
localizing and colocalizing subcategories of this category. Moreover, we prove
that -compact groups admit a homotopical form of Gorenstein duality.Comment: Corrected discussion of Chouinard's theorem for homotopical groups;
accepted for publication in Advances in Mathematic
Homotopy Theory
Algebraic topology in general and homotopy theory in particular is in an exciting period of growth and transformation, driven in part by strong interactions with algebraic geometry, mathematical physics, and representation theory, but also driven by new approaches to our classical problems. This workshop was a forum to present and discuss the latest result and ideas in homotopy theory and the connections to other branches of mathematics. Central themes of the workshop were derived algebraic geometry, homotopical invariants for ring spectra such as topological Hochschild homology, interactions with modular representation theory, group actions on spaces and the closely-related study of the classifying spaces of groups
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