The cohomology algebra of unordered configuration spaces

• Autores: Yves Félix, Daniel Tanré
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 72, Nº 2, 2005, págs. 525-544
• Idioma: inglés
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• Resumen

  • Given an -dimensional compact closed oriented manifold and a field , F. Cohen and L. Taylor have constructed a spectral sequence, , converging to the cohomology of the space of ordered configurations of points in . The symmetric group acts on this spectral sequence giving a spectral sequence of -differential graded commutative algebras. Here, an explicit description is provided of the invariants algebra of the first term of . This determination is applied in two directions.

    (a) In the case of a complex projective manifold or of an odd-dimensional manifold , the cohomology algebra of the space of unordered configurations of points in is obtained (the concrete example of is detailed).

    (b) The degeneration of the spectral sequence formed of the -invariants at level 2 is proved for any manifold .

    These results use a transfer map and are also true with coefficients in a finite field with .