Inverting the Hopf map

Homotopy Theory of Comodules over a Hopf Algebroid

Given a good homology theory E and a topological space X, E∗X is not just an E∗-module but also a comodule over the Hopf algebroid (E∗, E∗E). We establish a framework for studying the homological algebra of comodules over a well-behaved Hopf algebroid (A,Γ). That is, we construct the derived category Stable(Γ) of (A,Γ) as the homotopy category of a Quillen model structure on Ch(Γ), the category...

Single DV-DXCCII Based Voltage Controlled First Order All-pass Filter with Inverting and Non-inverting responses

In this paper, a new voltage controlled first order all-pass filter is presented. The proposed circuit employs a single differential voltage dual-X second generation current conveyor (DV-DXCCII) and a grounded capacitor only. The proposed all-pass filter provides both inverting and non inverting voltage-mode outputs from the same configuration simultaneously without any matching condition. Non-...

On the Coderivations of Some Hopf Algebras

Invariant elements in the dual Steenrod algebra

‎In this paper‎, ‎we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${mathcal{A}_p}^*$ under the conjugation map $chi$ and give bounds on the dimensions of $(chi-1)({mathcal{A}_p}^*)_d$‎, ‎where $({mathcal{A}_p}^*)_d$ is the dimension of ${mathcal{A}_p}^*$ in degree $d$‎.

A simplicial model for the Hopf map

We give an explicit simplicial model for the Hopf map S3 → S2. For this purpose, we construct a model of S3 as a principal twisted cartesian product K×ηS, where K is a simplicial model for S1 acting by left multiplication on itself, S2 is given the simplest simplicial model and the twisting map is η : ( S2 ) n → (K)n−1. We construct a Kan complex for the simplicial model K of S1. The simplicial...