Derived Group Completion

Sanjeevi Krishnan (May 19, 2016)

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Abstract

Every connected, finite CW complex is homotopy equivalent to the classifying space
of a monoid [McDuff, 1979], a set with an associative and unital multiplication. Thus group
completions of monoids correspond to fundamental groups of based spaces. We discuss concrete
algorithms for computing (co)homology and higher homotopy as algebraic constructions on
monoids.