Harnack-Thom Theorem for higher cycle groups and Picard varieties

Details Harnack-Thom Theorem for higher cycle groups and Picard varieties Harnack-Thom Theorem for higher cycle groups and Picard varieties

2005-09-07

arxiv.org/abs/math/0509149v3

Mathematics

Algebraic Geometry

22 pages, the case of divisors is computed. To appear in the Transaction of AMS

Scientific paper

We generalize the Harnack-Thom theorem to relate the ranks of the Lawson homology groups with $\Z_2$-coefficients of a real quasiprojective variety with the ranks of its reduced real Lawson homology groups. In the case of zero-cycle group, we recover the classical Harnack-Thom theorem and generalize the classical version to include real quasiprojective varieties. We use Weil's construction of Picard varieties to construct reduced real Picard groups, and Milnor's construction of universal bundles to construct some weak models of classifying spaces of some cycle groups. These weak models are used to produce long exact sequences of homotopy groups which are the main tool in computing the homotopy groups of some cycle groups of divisors. We obtain some congruences involving the Picard number of a nonsingular real projective variety and the rank of its reduced real Lawson homology groups of divisors.

Affiliated with

Also associated with

No associations

Rating

Harnack-Thom Theorem for higher cycle groups and Picard varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Harnack-Thom Theorem for higher cycle groups and Picard varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Harnack-Thom Theorem for higher cycle groups and Picard varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-215933