We obtain complete geometric invariants of cobordism classes of oriented simple fold maps of (n+ 1)-dimensional manifolds into an n-dimensional manifold N in terms of immersions with prescribed normal bundles. We compute that for N = R the cobordism group of simple fold maps is isomorphic to the direct sum of the (n−1)th stable homotopy group of spheres and the (n − 1)th stable homotopy group o...

This paper aims to prove two general fixed point theorems in multiplicative metric space (MMS) by using reciprocally continuous mappings and conditionally sequential absorbing mappings. Further our outcomes are validated discussing appropriate examples.

We consider the parameterized problem of counting all matchings with exactly k edges in a given input graph G. This problem is #W[1]-hard (Curticapean, ICALP 2013), so it is unlikely to admit f(k) · nO(1) time algorithms. We show that #W[1]-hardness persists even when the input graph G comes from restricted graph classes, such as line graphs and bipartite graphs of arbitrary constant girth and ...

We approach a problem of realising algebraic objects in certain universal equivariant stable homotopy theory; the global theory Schwede. Specifically, for ring spectrum $R$, we consider which classes homomorphisms $\eta_\ast\colon\pi_\ast^e R\rightarrow S_\ast$ can be realised by map $\eta\colon S$ category $R$-modules, and what multiplicative structures placed on $S$. If $\eta_\ast$ witnesses ...

It is shown that any left module A over a ring R can be written as the intersection of a downward directed system of injective submodules of an injective module; equivalently, as an inverse limit of one-to-one homomorphisms of injectives. If R is left Noetherian, A can also be written as the inverse limit of a system of surjective homomorphisms of injectives. Some questions are raised. The flat...

Let $\mathcal A$ be a unital $C^*$-algebra. We consider Jordan $*$-homomorphisms on $C(X, \mathcal A)$ and Lip$(X,\mathcal A)$. More precisely, for any $C^*$-algebra A$, we prove that every $*$-homomorph

We show that the theory of hyperrings, due to M. Krasner, supplies a perfect framework to understand the algebraic structure of the adèle class space HK = AK/K of a global field K. After promoting F1 to a hyperfield K, we prove that a hyperring of the form R/G (where R is a ring and G ⊂ R× is a subgroup of its multiplicative group) is a hyperring extension of K if and only if G ∪ {0} is a subfi...

The goal of this paper is to give an approach to constructing transfer homomorphisms along such maps π for abelian sheaves and presheaves of spectra which holds generally for the standard geometric topologies on the category Sch|S of schemes of finite type over S, satisfies the usual properties, and specializes to known phenomena. The construction displayed here, called the separable transfer, ...