7,164 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 homotopy fixed point set of Lie group actions on elliptic spaces
Let be a compact connected Lie group, or more generally a path connected
topological group of the homotopy type of a finite CW-complex, and let be a
rational nilpotent -space. In this paper we analyze the homotopy type of the
homotopy fixed point set , and the natural injection . We show that if is elliptic, that is, it has
finite dimensional rational homotopy and cohomology, then each path component
of is also elliptic. We also give an explicit algebraic model of the
inclusion based on which we can prove, for instance, that for a torus,
is injective in rational homotopy but, often, far from being a
rational homotopy equivalence.Comment: 32 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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