Let Sg be a general prime K3 surface in IP g of genus g ≥ 3 or a general double cover of IP 2 ramified along a sextic curve for g = 2 and Si,g its ith Veronese embedding. In this article we compute the corank of the Gaussian map ΦOSi,g (1) : ∧2 H(Si,g,OSi,g(1)) → H (Si,g,Ω 1 Si,g (2)) for i ≥ 2, g ≥ 2 and i = 1, g ≥ 17. The main idea is to reduce the surjectivity of ΦOSi,g (1) to an application...

Let $A_1$ be any spectrum in the class of finite spectra whose mod-2 cohomology is isomorphic to $\mathcal{A}(1)$ as a module over subalgebra Steenrod algebra; let $tmf$ connective topological modular forms. In this paper, we prove that $tmf$-Hurewicz image surjective.

It is known that the number of homomorphisms from a group $F$ to $G$ divisible by greatest common divisor order and exponent $F/[F,F]$. We investigate satisfying some natural conditions such as injectivity or surjectivity. The simplest nontrivial corollary our results following fact: {\it in any finite group, generating pairs $(x,y)$ $x^3=1=y^5$, multiple 15 $[G,G]\cdot\{g^{15}\;|\;g\in G\}$.

0 ∈ Tx + λCx, where T : D(T )⊂ X → 2X is a strongly quasibounded maximal monotone operator and C : D(C)⊂ X → X∗ satisfies the condition (S+)D(C) with L⊂ D(C). The method of approach is to use a topological degree theory for (S+)L-perturbations of strongly quasibounded maximal monotone operators, recently developed by Kartsatos and Quarcoo. Moreover, applying degree theory, a variant of the Fred...