On the cohomology of quotients of momentangle complexes
Abstract
We describe the cohomology of the quotient Z_K/H of a momentangle complex Z_K by a freely acting subtorus H in T^m by establishing a ring isomorphism of H*(Z_K/H,R) with an appropriate Toralgebra of the face ring R[K], with coefficients in an arbitrary commutative ring R with unit. This result was stated in [BP02, 7.37] for a field R, but the argument was not sufficiently detailed in the case of nontrivial H and finite characteristic. We prove the collapse of the corresponding EilenbergMoore spectral sequence using the extended functoriality of Tor with respect to `strongly homotopy multiplicative' maps in the category DASH, following Munkholm [Mu74]. Our collapse result does not follow from the general results of GugenheimMay and Munkholm.
 Publication:

arXiv eprints
 Pub Date:
 June 2015
 DOI:
 10.48550/arXiv.1506.06875
 arXiv:
 arXiv:1506.06875
 Bibcode:
 2015arXiv150606875P
 Keywords:

 Mathematics  Algebraic Topology
 EPrint:
 3 pages