Related papers: An equivariant surgery classification of $C_p$-sur…

For an odd prime $p$, we determine the $p$-primary component of the Farrell cohomology of the pure mapping class groups of a non orientable surface of genus $p$ with $k\geqslant 1$ marked points. To do this, we classify conjugacy classes of…

We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomology for actions of transitive topological groupoids. We show…

In this article we prove that the full automorphism group of a cyclic $p$-gonal pseudo-real Riemann surface of genus $g$ is either a semidirect product $C_{n}\ltimes C_{p}$ or a cyclic group, where $p$ is a prime $>2$ and $g>(p-1)^{2}$. We…

We give a complete calculation of the cobordism ring of stably almost complex $C_p$-manifolds in terms of generators and relations. We also compare these generators with the geometrically-defined generators obtained by Kosniowski.

Let $p$ be a fixed prime number and let $R$ denote a uniserial $p$-adic space group of dimension $d_x=(p-1)p^{x-1}$ and with cyclic point group of order $p^x$. In this short note we prove that all the quotients of $R$ of size bigger than or…

We introduce a new generalization of Gompf nuclei and give applications. We construct infinitely many exotic smooth structures for a large class of compact 4-manifolds with boundary, regarding topological invariants. We prove that a large…

We introduce Clifford Group Equivariant Neural Networks: a novel approach for constructing $\mathrm{O}(n)$- and $\mathrm{E}(n)$-equivariant models. We identify and study the $\textit{Clifford group}$, a subgroup inside the Clifford algebra…

Given a symplectic manifold $M$, we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of $(\bar{M})^k\times M$ via symplectic reduction. If $M$ is also a symplectic groupoid, then its multiplication…

Let p denote an odd prime. For all p-admissible conductors c over a quadratic number field \(K=\mathbb{Q}(\sqrt{d})\), p-ring spaces \(V_p(c)\) modulo c are introduced by defining a morphism \(\psi:\,f\mapsto V_p(f)\) from the divisor…

We define a new variety of loops we call $\Gamma$-loops. After showing $\Gamma$-loops are power associative, our main goal will be showing a categorical isomorphism between Bruck loops of odd order and $\Gamma$-loops of odd order. Once this…

In this article we study graded Clifford algebras with a gradation preserving action of automorphisms given by $H_p$, the Heisenberg group of order $p^3$ with $p$ prime. After reviewing results in dimensions 3 and 4, we will determine the…

Let $p$ be an odd prime, and $D_{2p}=\langle \tau,\sigma\mid \tau^p=\sigma^2=e,\sigma\tau\sigma=\tau^{-1}\rangle$ the dihedral group of order $2p$. In this paper, we provide the number of (connected) Cayley (di-)graphs on $D_{2p}$ up to…

Let P be a connected smooth p-manifold. We describe the group of all cobordism classes of smooth maps of n-manifolds to P with singularities of a given $cal K$-invariant class in terms of certain stable homotopy groups by applying the…

In [R2] and [RO] the Arnold conjecture for closed symplectic manifolds with trivial second homotopy group was proved. This proof used surgery and cobordism theory. Here we give a purely cohomological proof of this result.

We prove the following result: Let $(M,g_0)$ be a complete noncompact manifold of dimension $n\geq 12$ with isotropic curvature bounded below by a positive constant, with scalar curvature bounded above, and with injectivity radius bounded…

Closed (and simply-connected) manifolds whose dimensions are greater than 4 are classified via sophisticated algebraic and abstract theory such as surgery theory and homotopy theory. It is difficult to handle 3 or 4-dimensional closed…

We develop a categorical index calculus for elliptic symbol families. The categorified index problems we consider are a secondary version of the traditional problem of expressing the index class in K-theory in terms of…

We study groups of C^1 orientation-preserving homeomorphisms of the plane, and pursue analogies between such groups and circularly-orderable groups. We show that every such group with a bounded orbit is circularly-orderable, and show that…

In a previous paper, we have constructed, for an arbitrary Lie group G and any of the fields F=R or C, a good equivariant cohomology theory KF_G^*(-) on the category of proper $G$-CW-complex and have justified why it deserved the label…

The principal filtration of the infinite-dimensional odd Contact Lie superalgebra over a field of characteristic $p>2$ is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain…