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A general comparison theorem for $p$-harmonic maps in homotopy class     comparison theorem  homotopy class       font style='font-size:12px;'> 2010/11/22
We prove a general comparison result for homotopic finite $p$-energy $C^{1}$ $p$-harmonic maps $u,v:M\to N$ between Riemannian manifolds, assuming that $M$ is $p$-parabolic and $N$ is complete and non...
We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an A_infty functor from the representations up to homotopy of a Lie algebroid to those of its infin...
Relative categories: Another model for the homotopy theory of homotopy theories     model  homotopy theory       font style='font-size:12px;'> 2010/11/12
We lift Charles Rezk's complete Segal space model structure on the category of simplicial spaces to a Quillen equivalent one on the category of relative categories.
Stable A^1-homotopy and R-equivalence     Stable A^1-homotopy  R-equivalence       font style='font-size:12px;'> 2010/11/19
We prove that existence of a k-rational point can be detected by the stable A^1-homotopy category of S^1-spectra
Homotopy Theory for C^{*}-algebras     Homotopy Theory  math       font style='font-size:12px;'> 2010/11/19
Category of fibrant objects is a convenient framework to do homotopy theory, introduced and developed by Ken Brown. In this paper, we apply it to the category of C^{*}-algebras. In particular, we get...
On [L]-homotopy groups     On [L]-homotopy groups  homotopy group        font style='font-size:12px;'> 2010/10/29
Some properties of [L]-homotopy group for finite complex L are investigated. It is proved that for complex L whose extension type lying between Sn and Sn+1 n-th [L]-homotopy group of Sn is isomorphic ...
We construct a functor from the derived category of homotopy Gerstenhaber algebras with finite-dimensional cohomology to the purely geometric category of so-called $F_{\infty}$-manifolds. The latter ...

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