## Homology, Homotopy and Applications

- Homology Homotopy Appl.
- Volume 9, Number 2 (2007), 1-17.

### Homotopy spectral sequences of pointed simplicial spaces

#### Abstract

Using simplicial machinery, which is analogous to that developed by
Bousfield-Kan, we describe a first quadrant homotopy spectral sequence for a
termwise connected pointed simplicial space *X* in terms of differential
relations on the normalized homotopy of *X* and establish the existence of
a smash product pairing.

#### Article information

**Source**

Homology Homotopy Appl., Volume 9, Number 2 (2007), 1-17.

**Dates**

First available in Project Euclid: 23 January 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1201127330

**Mathematical Reviews number (MathSciNet)**

MR2320770

**Zentralblatt MATH identifier**

1156.55016

**Subjects**

Primary: 55T05: General

Secondary: 18G30: Simplicial sets, simplicial objects (in a category) [See also 55U10] 18G55: Homotopical algebra 55P65: Homotopy functors

**Keywords**

Homotopy spectral sequence smash product pairing

#### Citation

Paluch, Michael. Homotopy spectral sequences of pointed simplicial spaces. Homology Homotopy Appl. 9 (2007), no. 2, 1--17. https://projecteuclid.org/euclid.hha/1201127330