The stable cohomology of self-equivalences of connected sums of products of spheres

Abstract

We identify the cohomology of the stable classifying space of homotopy automorphisms (relative to an embedded disk) of connected sums of $S^k\times S^l$, where $3\le k<l\le 2k-2$. The result is expressed in terms of Lie graph complex homology.

arXiv comment63 pages. Version 2: Used a result of Li and Sun to simplify the proof and improve the stable range of the main result. Version 3: Generalized parts of the paper to apply to certain non-trivial coefficients. Version 4: Small correction; pre-copyediting version. Version 5: Used numbering of published version

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Cited by in corpus (4)

• Higher structures in rational homotopy theory
• Algebraic models for classifying spaces of fibrations
• Some rational homology computations for diffeomorphisms of odd-dimensional manifolds
• Representation stability for homotopy automorphisms