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Homotopy theory, homological algebra, algebraic treatments of manifolds.

2 votes
0 answers
213 views

Why is cellularization the fiber of nullification for slice cells?

I'm a bit confused about the nullification functors that come up when constructing the slice tower in HHR. Let $\mathcal{A}$ be a set of compact objects in the $G$-equivariant stable homotopy category …
Christian Wimmer's user avatar
2 votes
2 answers
391 views

Smashing with a cw-complex preserves weak equivalences between well-pointed spaces

By well-pointed i mean that the inclusion of the base point is a h-cofibration, weak equivalences are the usual weak homotopy equivalences between spaces. this is claimed as part of theorem 6.9 (i) in …
Christian Wimmer's user avatar
8 votes
1 answer
893 views

Representing KO-theory using Clifford algebras

I'm trying to understand a statement Segal makes in this book: Let $C_q$ be the real Clifford algebra associated to the standard negative definite form on $\mathbb{R^q}$ and let $\Phi_q(n)$ be the sp …
Christian Wimmer's user avatar
14 votes
1 answer
544 views

Homotopy fixed points of complex conjugation on $BU(n)$

Stably it is known that $(\mathbb Z\times BU)^{hC_2}\simeq \mathbb Z\times BO$ holds. The homotopy fixed point spectral sequence for KU with complex conjugation action can be completely calculated and …
Christian Wimmer's user avatar
4 votes
1 answer
562 views

Homotopy colimit of a simplicial DGA

It seems to be well-known that the homotopy colimit of a simplicial chain complex (unbounded) can be computed by taking the totalization of the associated (half-plane) double complex. The totalization …
Christian Wimmer's user avatar