A course in some aspects of classical homotopy theory

1987 ◽  
pp. 1-92 ◽  
Author(s):  
F. R. Cohen
Keyword(s):  
Homotopy Theory ◽  
Classical Homotopy

Numerical Invariants in Homotopical Algebra, I

1975 ◽  
Vol 27 (4) ◽  
pp. 901-934 ◽  
Author(s):  
K. Varadarajan
Keyword(s):  
Homotopy Theory ◽  
Algebra I ◽  
Homotopical Algebra ◽  
Numerical Invariants ◽  
Set Up ◽  
Lusternik Schnirelmann ◽  
Classical Homotopy

Classically CW-complexes were found to be the best suited objects for studying problems in homotopy theory. Certain numerical invariants associated to a CW-complex X such as the Lusternik-Schnirelmann Category of X, the index of nilpotency of ᘯ(X), the cocategory of X, the index of conilpotency of ∑ (X) have been studied by Eckmann, Hilton, Berstein and Ganea, etc. Recently D. G. Quillen [6] has developed homotopy theory for categories satisfying certain axioms. In the axiomatic set up of Quillen the duality observed in classical homotopy theory becomes a self-evident phenomenon, the axioms being so formulated.

scholarly journals On the Cohomology of the Mapping Class Group of the Punctured Projective Plane

2020 ◽  
Vol 71 (2) ◽  
pp. 539-555
Author(s):  
Miguel A Maldonado ◽  
Miguel A Xicoténcatl
Keyword(s):  
Exact Sequence ◽  
Configuration Space ◽  
Mapping Class Group ◽  
Homotopy Theory ◽  
Class Group ◽  
Orientable Surface ◽  
Configuration Spaces ◽  
Mapping Class ◽  
Serre Spectral Sequence ◽  
Classical Homotopy

Abstract The mapping class group $\Gamma ^k(N_g)$ of a non-orientable surface with punctures is studied via classical homotopy theory of configuration spaces. In particular, we obtain a non-orientable version of the Birman exact sequence. In the case of ${\mathbb{R}} \textrm{P}^2$, we analyze the Serre spectral sequence of a fiber bundle $F_k({\mathbb{R}}{\textrm{P}}^{2}) / \Sigma _k \to X_k \to BSO(3)$ where $X_k$ is a $K(\Gamma ^k({\mathbb{R}} \textrm{P}^2),1)$ and $F_k({\mathbb{R}}{\textrm{P}}^{2}) / \Sigma _k$ denotes the configuration space of unordered $k$-tuples of distinct points in ${\mathbb{R}} \textrm{P}^2$. As a consequence, we express the mod-2 cohomology of $\Gamma ^k({\mathbb{R}} \textrm{P}^2)$ in terms of that of $F_k({\mathbb{R}}{\textrm{P}}^{2}) / \Sigma _k$.

Categorical Homotopy Theory

2009 ◽  
Author(s):  
Emily Riehl
Keyword(s):  
Homotopy Theory

On the Homotopy Theory of Arrangements

2018 ◽  
Author(s):  
Michael Falk ◽  
Richard Randell
Keyword(s):  
Homotopy Theory

On the homotopy theory of arrangements, II

2018 ◽  
Author(s):  
Michael Falk ◽  
Richard Randell
Keyword(s):  
Homotopy Theory
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