Webinduce (multiplicative) abstract Postnikov towers for algebras over ∞-operads. As the basis of our inductive proof, we show that the Postnikov tower of spaces is part of a … In homotopy theory, a branch of algebraic topology, a Postnikov system (or Postnikov tower) is a way of decomposing a topological space's homotopy groups using an inverse system of topological spaces whose homotopy type at degree $${\displaystyle k}$$ agrees with the truncated … Meer weergeven A Postnikov system of a path-connected space $${\displaystyle X}$$ is an inverse system of spaces with a sequence of maps 1. The … Meer weergeven One application of the Postnikov tower is the computation of homotopy groups of spheres. For an $${\displaystyle n}$$-dimensional sphere $${\displaystyle S^{n}}$$ we can use the Hurewicz theorem to show each $${\displaystyle S_{i}^{n}}$$ is … Meer weergeven The dual notion of the Whitehead tower can be defined in a similar manner using homotopy fibers in the category of spectra. If we let Meer weergeven Postnikov tower of a K(G,n) One of the conceptually simplest cases of a Postnikov tower is that of the Eilenberg–Maclane space $${\displaystyle K(G,n)}$$. This gives a tower with Postnikov … Meer weergeven Given a CW complex $${\displaystyle X}$$, there is a dual construction to the Postnikov tower called the Whitehead tower. Instead of killing off all higher homotopy groups, the Whitehead tower iteratively kills off lower homotopy groups. This is given … Meer weergeven • Adams spectral sequence • Eilenberg–MacLane space • CW complex • Obstruction theory • Stable homotopy theory Meer weergeven
On the Postnikov towers for real and complex connective K-theory
WebDOI (Digital Object Identifier) 10.1007/s102310100015 Annali di Matematica 180, 331–358 (2001) Alberto Cavicchioli · Fulvia Spaggiari On the homotopy type of Poincare spaces´ WebConvergence of Voevodsky’sSlice Tower 911 Conjecture 5.Let k be a field of finite virtual 2-cohomological dimension. Then the I(k)-completed slice tower is weakly convergent: after I(k)-completion, the filtration Fil∗ TateΠr,qfmEis stalkwise separated for each Ein SHfin(k) and each r,q,m. This modified conjecture is equivalent to Voevodsky’s convergence … couch in breakfast room
Whitehead tower in nLab
WebThe map induced in cohomology by 1 implies that the left hand map ko! HZ is nontrivial. This implies that the ber of c 2 is koh1i, giving the next Postnikov lift of the cRsequence. HZ / 2HF 2 Sq1 / HZ / 2HZ 1ko O /koh1i O c 1 / 2ku O r / 2ko O koh1i O 2 /koh2i O c 2 / 4ku O r 1 / 2koh1i O Again we need to record the maps induced in cohomology ... Webis a construction of a canonical Postnikov tower for any motivic spectrum E. The quotients of this tower s; (E) are called the slices of E and, by construction, there is a spectral sequence whose E2-term is given by the cohomology theories represented by the slices and which attempts to converge to the theory represented by E. For WebON THE POSTNIKOV TOWERS FOR REAL AND COMPLEX CONNECTIVE K-THEORY ROBERT R. BRUNER 1. Introduction The analysis of real connective K-theory is facilitated by the ‘ηcR’ cofiber sequence η ko −→c ku −→R Σ2ko relating real and complex K-theories [2]. Here we extend this relationship through the Postnikov towers, producing several ... couch indentation