Maurizio Brunetti

The K(n)-Euler characteristic of extraspecial p-groups

Let p be an odd prime, and let K(n)∗ denote the nth Morava K-theory at the prime p; we compute the K(n)-Euler characteristic χn,p(G) of the classifying space of an extraspecial p-group G. Equivalently, we get the number of conjugacy classes of commuting n-tuples in the group G. We obtain this result by examining the lattice of isotropic subspaces of an even-dimensional Fp-vector space with respect to a non-degenerate alternating form B.

Connected signed graphs L-cospectral to signed ∞-graphs

ABSTRACT A signed graph is a pair , where is a graph and is the sign function on the edges of G. For a signed graph we consider the Laplacian matrix defined as , where is the matrix of vertex degrees of G and the (signed) adjacency matrix . A signed ∞-graph consists of two signed cycles with just one vertex in common. In this paper, we study the Laplacian spectral determination problem for the class of signed ∞-graphs, and we identify all connected L-cospectral mates.