# Algebraic Topology from a Homotopical Viewpoint

@inproceedings{Aguilar2002AlgebraicTF, title={Algebraic Topology from a Homotopical Viewpoint}, author={Marcelo A. Aguilar and Samuel Carlos Gitler and Carlos Prieto}, year={2002} }

Introduction.- Basic Concepts and Notation.- Function Spaces.- Connectedness and Algebraic Invariants.- Homotopy Groups.- Homotopy Extension and Lifting Properties.- CW-Complexes Homology.- Homotopy Properties of CW-Complexes.- Cohomology Groups and Related Topics.- Vector Bundles.- K-Theory.- Adams Operations and Applications.- Relations Between Cohomology and Vector Bundles.- Cohomology Theories and Brown Representability.- Appendix A: Proof of the Dold-Thom Theorem.- Appendix B: Proof of the…

## 134 Citations

A Homology and Cohomology Theory for Real

- Mathematics
- 2010

In this paper we develop homology and cohomol- ogy theories which play the same role for real projective vari- eties that Lawson homology and morphic cohomology play for projective varieties…

Cubical Homotopy Theory

- Mathematics
- 2015

Preface Part I. Cubical Diagrams: 1. Preliminaries 2. 1-cubes: homotopy fibers and cofibers 3. 2-cubes: homotopy pullbacks and pushouts 4. 2-cubes: the Blakers-Massey Theorems 5. n-cubes: generalized…

Introduction to Stable homotopy theory -- 2 in nLab

- Mathematics
- 2016

We give an introduction to the stable homotopy category and to its key computational tool, the Adams spectral sequence. To that end we introduce the modern tools, such as model categories and highly…

A homology and cohomology theory for real projective varieties

- Mathematics
- 2005

In this paper we develop homology and cohomology theories which play the same role for real projective varieties that Lawson homology and morphic cohomology play for projective varieties…

Topological Abelian Groups and Equivariant Homology

- Mathematics
- 2008

We prove an equivariant version of the Dold–Thom theorem by giving an explicit isomorphism between Bredon–Illman homology and equivariant homotopical homology π*(F G (X, L)), where G is a finite…

Suspensions of crossed and quadratic complexes, CO-H-structures and applications

- Mathematics
- 2004

Crossed and quadratic modules are algebraic models of the 2-type and the 3-type of a space, respectively. In this paper we compute a purely algebraic suspension functor from crossed to quadratic…

Acyclicity in Algebraic K-theory

- Mathematics
- 2016

The central topic of this work is the concept of acyclic spaces in topological K-theory and their analogues in algebraic K-theory. We start by describing topological Ktheory and some basic results,…

THE INFINITE SYMMETRIC PRODUCT AND HOMOLOGY THEORY

- Mathematics
- 2010

Following the work of Aguilar, Gitler, and Prieto, I define the infinite symmetric product of a pointed topological space. The infinite symmetric product allows the construction of a reduced homology…

A proof of the Dold$-$Thom theorem via factorization homology

- Mathematics
- 2017

The Dold$-$Thom theorem states that for a sufficiently nice topological space, M, there is an isomorphism between the homotopy groups of the infinite symmetric product of M and the homology groups of…

Discrete homotopy of token configurations

- Mathematics
- 2020

This paper studies graphical analogs of symmetric products and unordered configuration spaces in topology. We do so from the perspective of the discrete homotopy theory introduced by Barcelo et al.…