In previous work, the authors have each introduced methods for studying the 2-line of the p-local Adams-Novikov spectral sequence in terms of the arithmetic of modular forms. We give the precise relationship between the congruences of modular forms introduced by the first author with the Qspectrum and the f -invariant of the second author. This relationship enables us to refine the target group...

This section contains statements of our results on homotopy operations as well as some applications of these results. The proofs depend on material in §2 and will be given in §3Note that, aside from the computations in ~,S at the end of this section, all the results here apply to the homotopy of any H ring spectrum Y. Let ~:DpY + Y denote the structure map. The order of results in this section ...

let $g = (v, e)$ be a simple graph. denote by $d(g)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $a(g)$ the adjacency matrix of $g$. the  signless laplacianmatrix of $g$ is $q(g) = d(g) + a(g)$ and the $k-$th signless laplacian spectral moment of  graph $g$ is defined as $t_k(g)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

We investigate the relations between Grothendieck group of coherent modules an algebraic variety and its Chow cycles modulo rational equivalence. Those are in essence torsion phenomena, which we attempt to control by considering action Adams operations on Brown-Gersten-Quillen spectral sequence related objects, such as connective K_0-theory. provide elementary arguments whenever possible. As ap...

where f2. G is an appropriate cobordism theory of immersed submanifolds of Euclidean space. By generalizing techniques of Browder [2] we shall give necessary and sufficient Adams spectral sequence conditions for an element in t2. G to have nonzero Kervaire invariant. Also we will prove that for every j > 1 there exists a closed, differentiable manifold of dimension 2 ) § together with an immers...

This work focuses on a generalization of the models for rational homotopy theory developed by D. Sullivan and D. Quillen and p-adic homotopy developed by M. Mandell to K(1)-local homotopy theory. The work is divided into two parts. The first part is a reflection on M. Mandell's model for p-adic homotopy theory. Reformulating M. Mandell's result in terms of an adjunction between p-complete, nilp...

Abstract We prove that there is no parity anomaly in M-theory the low-energy field theory approximation. Our approach computational. determine generators for 12-dimensional bordism group of pin manifolds with a w1-twisted integer lift w4; these are on which Wick-rotated exists. The cancellation comes down to computing specific η-invariant and cubic form manifolds. Of interest beyond this proble...

We provide several constructions in differential KO-theory. First, we construct a refinement of the Aˆ-genus and pushforward leading to Riemann-Roch theorem. set up Atiyah-Hirzebruch spectral sequence (AHSS) for KO-theory explicitly identify differentials, including ones which mix geometric topological data. highlight power these explicit identifications by providing characterization forms imag...