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Some characterizations of acyclic maps

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arxiv 1711.08898 v2 pith:O5NMIHCH submitted 2017-11-24 math.AT math.KT

G. Raptis This is my paper · ORCID
classification math.ATmath.KT
keywords acyclichomotopymapscategoricalcharacterizationsclassdiscussmodality
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We discuss two categorical characterizations of the class of acyclic maps between (path-connected) spaces. The first one is in terms of the higher categorical notion of an epimorphism. The second one employs the notion of a balanced map, that is, a map whose homotopy pullbacks define also homotopy pushouts. We also identify the modality in the homotopy theory of spaces that is defined by the class of acyclic maps, and discuss the content of the generalized Blakers-Massey theorem for this modality.

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  1. Modules over algebraic cobordism

    math.AG 2019-08 accept novelty 8.0 of 10

    MGL-modules over a scheme are equivalent to motivic spectra with finite syntomic transfers, and the infinite P^1-loop space of MGL is the A^1-homotopy type of the moduli stack of finite syntomic schemes.

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