Postnikov pieces and 𝐵ℤ/𝕡-homotopy theory

Castellana, Natàlia; Crespo, Juan A.; Scherer, Jérôme

doi:10.1090/s0002-9947-06-03957-2

Cited by 7 publications

(7 citation statements)

References 20 publications

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“…Hence,

f

is a

B Z / p^{\infty}

‐equivalence and so

C W_{B Z / p^{\infty}} false(B P false) ≃ C W_{B Z / p^{\infty}} false(B P_{0} false) ≃ B P_{0}

. The map

B {normalΩ}_{p^{m}} false(P false) \to B P

induced by the inclusion

{normalΩ}_{p^{m}} false(P false) ⩽ P

is a

B Z / p^{m}

‐equivalence since

{map}_{*} false(B double-struckZ / p^{m}, B P false) ≃ Hom false(double-struckZ / p^{m}, P false) = Hom false(double-struckZ / p^{m}, Ω_{p^{m}} P false) ≃ {map}_{*} false(B double-struckZ / p^{m}, B Ω_{p^{m}} (P) false)

, and finally

B {normalΩ}_{p^{m}} P

B Z / p^{m}

‐cellular according to [, Corollary 2.5].

□

…”

Section: Cellularization Of Classifying Spaces Of Discrete P‐toral Grmentioning

confidence: 99%

“…Moreover,

o false(y false) = o false(y x^{- 1} false) = 4

y x^{- 1} y x^{- 1} = y y x x^{- 1} = y^{2}

. Hence,

B Q_{2^{n + 1}}

B Z / 4

‐cellular for all

n ⩾ 2

according to [, Corollary 2.5]. For

n = 1

Q_{4} = false⟨ x, y false⟩

, where

o (x) = o (y) = 2

, so

B Q_{4}

B Z / 2

‐cellular and, in particular,

B Z / 4

‐cellular.…”

Section: Cellularization Of Classification Spaces Of Compact Lie Groupsmentioning

confidence: 99%

“…Proof We follow the ideas in [, Proposition 2.4]. Let

m

be any non‐negative integer and consider Chachólski's fibre sequence

C W_{B_{m}} false(B P false) \overset{c}{\to} B P \overset{r}{\to} P_{Σ B_{m}} C .

If the map

r

is null‐homotopic, then the homotopy fibre is

C W_{B_{m}} false(B P false) ≃ B P \times Ω false(P_{normalΣ B_{m}} C false)

.…”

Section: Cellularization Of Classifying Spaces Of Discrete P‐toral Grmentioning

confidence: 99%

See 2 more Smart Citations

Cellular approximations of p‐local compact groups

Castellana

Flores

Gavira-Romero

2019

Journal of Topology

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“…Hence,

f

is a

B Z / p^{\infty}

‐equivalence and so

C W_{B Z / p^{\infty}} false(B P false) ≃ C W_{B Z / p^{\infty}} false(B P_{0} false) ≃ B P_{0}

. The map

B {normalΩ}_{p^{m}} false(P false) \to B P

induced by the inclusion

{normalΩ}_{p^{m}} false(P false) ⩽ P

is a

B Z / p^{m}

‐equivalence since

{map}_{*} false(B double-struckZ / p^{m}, B P false) ≃ Hom false(double-struckZ / p^{m}, P false) = Hom false(double-struckZ / p^{m}, Ω_{p^{m}} P false) ≃ {map}_{*} false(B double-struckZ / p^{m}, B Ω_{p^{m}} (P) false)

, and finally

B {normalΩ}_{p^{m}} P

B Z / p^{m}

‐cellular according to [, Corollary 2.5].

□

…”

Section: Cellularization Of Classifying Spaces Of Discrete P‐toral Grmentioning

confidence: 99%

“…Moreover,

o false(y false) = o false(y x^{- 1} false) = 4

y x^{- 1} y x^{- 1} = y y x x^{- 1} = y^{2}

. Hence,

B Q_{2^{n + 1}}

B Z / 4

‐cellular for all

n ⩾ 2

according to [, Corollary 2.5]. For

n = 1

Q_{4} = false⟨ x, y false⟩

, where

o (x) = o (y) = 2

, so

B Q_{4}

B Z / 2

‐cellular and, in particular,

B Z / 4

‐cellular.…”

Section: Cellularization Of Classification Spaces Of Compact Lie Groupsmentioning

confidence: 99%

See 1 more Smart Citation

Cellular approximations of p‐local compact groups

Castellana

Flores

Gavira-Romero

2019

Journal of Topology

Self Cite

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“…For a connected H-space X such that Ω n X is BZ/p-local, the study of the homotopy type of map * (BZ/p, X) is drastically simplified by Theorem 3.2, since this space is equivalent to map * (BZ/p, F ) where F is a Postnikov piece, as we explain in the proof below. A complete study of the BZ/p-homotopy theory of such H-spaces is undertaken in [13].…”

Section: Bousfield's Bz/p-nullification Filtrationmentioning

confidence: 99%

Deconstructing Hopf spaces

2006

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“…The functor CW A turns out to be augmented and idempotent and is characterized by the facts that map * (A, CW A X) is weakly homotopy equivalent to map * (A, X) and every map A → X factors through CW A X in a unique way, up to homotopy. These ideas have made a great impact both in Homotopy Theory ( [CDI06], [CCS07], [RS08]) and outside of it, because they can be generalized in a natural way to any framework where there is a notion of limit (see examples in [DGI01], [BKI08] or [Kie08]). A line of research of great relevance in the last years, and very related to our work, is cellular approximation in the category of groups ([RS01], [Flo07], [DGS07], [DGS08]).…”

Section: Introductionmentioning

confidence: 99%