60 research outputs found
rational homotopy of mapping spaces
In this paper we describe explicit algebras modeling the rational
homotopy type of any component of the spaces \map(X,Y) and \map^*(X,Y) of
free and pointed maps between the finite nilpotent CW-complex and the
finite type nilpotent CW-complex . When is of finite type, non
necessarily finite, we also show that the algebraic covers of these
algebras model the universal covers of the corresponding mapping spaces.Comment: 19 page
The gauge action, DG Lie algebra and identities for Bernoulli numbers
In this paper we prove a family of identities for Bernoulli numbers
parameterized by triples of integers with , .
These identities are deduced while translating into homotopical terms the gauge
action on the Maurer Cartan Set which can be seen an abstraction of the
behaviour of gauge infinitesimal transformations in classical gauge theory. We
show that Euler and Miki's identities, well known and apparently non related
formulas, are linear combinations of our family and they satisfy a particular
symmetry relation.Comment: Small modifications. To appear in Forum Mathematicu
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