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Homotopy type through homology groups

Omar Antolín Camarena, Andrés Carnero Bravo

Abstract

We show that if a complex has free finitely generated reduced homology groups for two consecutive dimensions and trivial homology for all other dimensions, then it must have the homotopy type of a wedge of spheres of two consecutive dimensions. We also show other pairs of dimensions for which the last result can be generalized.

Homotopy type through homology groups

Abstract

We show that if a complex has free finitely generated reduced homology groups for two consecutive dimensions and trivial homology for all other dimensions, then it must have the homotopy type of a wedge of spheres of two consecutive dimensions. We also show other pairs of dimensions for which the last result can be generalized.
Paper Structure (2 theorems, 13 equations)

This paper contains 2 theorems, 13 equations.

Key Result

Theorem 1

Let $X$ be a simply connected CW-complex such that the only non-zero reduced homology group is $\tilde{H}_d(X)\cong\mathbb{Z}^a$. Then

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof