比利时vs摩洛哥足彩
,
university of california san diego
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algebraic geometry seminar
michael mcquillan
universita di roma tor vergata/ihes
2-galois theory
abstract:
a theorem of whitehead asserts that the topological 2-type of a (connected) space is uniquely characterised by the triple ($\pi_1, \pi_2, k_3$), where the $\pi_i, i\leq 2$ are the homotopy groups $\pi_i, i\leq 2, k_3$ is the postnikov class $\in h^3$($pi_1, \pi_2$), and, indeed all such triples may be realised. such triples are synonymous with a 2-group, $\pi_2$, i.e. a group `object' in the category of categories, which plays the same role for 2-types as the fundamental group does for 1-types. in particular, there is a 2-galois correspondence between the 2-category of champs which are etale fibrations over a space and $\pi_2$ equivariant groupoids generalising the usual 1-galois correspondence between spaces which are etale fibrations over a given space and $\pi_1$ equivariant sets. the talk will explain the pro-finite analogue of this correspondence, so, albeit only for the 2-type, a much simpler and more generally valid description of the etale homotopy than that of artin-mazur.
host: james mckernan
may 16, 2014
2:30 pm
ap&m 7218
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