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Apr
17
comment Does the category of G-spectra know G?
Re. the question of "why not use some nonabelian coefficients like all $G$-spaces", the point for me is that my access to the category of $G$-modules comes via constructible sheaves on a space with fundamental group $G$. Of course, one can take constructible sheaves with nonabelian coefficients. However, I need to use microlocal techniques in sheaf theory, which fundamentally depend on the ability to take cones, shifts, etc. Thus, I need to use coefficients which allow this; ergo, spectra rather than spaces.
Apr
17
awarded  Nice Question
Apr
16
revised Does the category of G-spectra know G?
edited tags
Apr
16
accepted What does the representation category of the knot group know?
Apr
16
comment Does the category of G-spectra know G?
@AntonFetisov : but what is the stabilization of G? How do you know it doesn't know G? (Finding a finite group counter example to Z[G] knows G took 60 years or something)
Apr
16
revised What does the representation category of the knot group know?
added 45 characters in body
Apr
16
answered What does the representation category of the knot group know?
Apr
16
asked Does the category of G-spectra know G?
Apr
6
comment On push-forward of the constant sheaf for fibrations
Consider the Hopf fibration $S^3 \to S^2$. If your sequence split, then $H^*(S^2)$ would be a summand of $H^*(S^3)$.
Apr
1
comment What kind of K-theory is this?
Eg how is it related to any usual notion of k theory, in particular, is it just equal to one of them.
Mar
31
asked What kind of K-theory is this?
Mar
19
comment Does the “holomorphic spheres-to-continuous spheres” forgetful function respect the mixed Hodge structures on homotopy groups?
Is this mixed hodge structure constructed by actually making a simplicial scheme (which?) whose cohomology groups are the homotopy groups of the original $X$?
Mar
19
comment N-periodic derived categories
Is it not OK to just work in the usual Z-graded but unbounded derived category, and then pass to fixed points under shift-by-N?
Mar
18
awarded  Yearling
Nov
24
awarded  Civic Duty
Nov
7
revised What does the representation category of the knot group know?
deleted 94 characters in body
Nov
7
comment What does the representation category of the knot group know?
representation of one, representation of the other, morphism between them compatible with the map of groups.
Nov
6
asked What does the representation category of the knot group know?
Nov
5
awarded  Mortarboard
Nov
5
awarded  Enlightened