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On the homology of mapping spaces

Semën Podkorytov (2011)

Open Mathematics

Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.

On the space of maps inducing isomorphic connections

T. R. Ramadas (1982)

Annales de l'institut Fourier

Let ω be the universal connection on the bundle E U ( n ) B U ( n ) . Given a principal U ( n ) -bundle P M with connection A , we determine the homotopy type of the space of maps ϕ of M into B U ( n ) such that ( ϕ + E U ( n ) , ϕ + ω ) is isomorphic to ( P , A ) . Here ϕ + denotes pull-back.

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