Every -complex is homotopy equivalent to (the realization of) a simplicial complex.

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#
algebraic topology

# This’ a glue problem

# Skip the sphere

# Drawable 3-manifolds

# Three-sheeted connected covering spaces of the wedge of three real projective spaces

Every -complex is homotopy equivalent to (the realization of) a simplicial complex.

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Compute the homotopy groups of the compact surfaces.

For an embedded compact 3-manifold , implies .

The title is pretty self-explanatory: the exercise is to classify such coverings.