Let $T$ be the category of compactly generated weak Hausdorff spaces with model structure given by Serre fibrations, Serre cofibrations and weak homotopy equivalences. Let $G = |G. …

Let $A$ and $B$ square real matrices. I know that the matrix $A+B$ has 1 as eigenvalue of multiplicity 1 and the others eigenvalues have their modulus <1. Can we say something a …

A Morse funnction on a smooth manifold is usually intuitively interpreted as follows: Imagine the manifold to be a mountainous landscape and the Morse function as the elevation of …

Are there tetrahedra which can be subdivided into three parts similar to the original? I believe this would require splitting one face into three parts. I know some types of tetrah …

Let $X$ be a sympletic manifold and $A\in H_2(X;\mathbb{Q})$. Let $g$ and $k$ be nonnegative integers. Assume that $$\mathcal{M}_{g,k}(X;A)$$ is dense in $$\overline{\mathcal{M}} …

Note: This question was posted in error, and should be closed as no longer relevant. The correct question is posted at http://mathoverflow.net/questions/131353/help-with-this-sys …

I define the notion of "Galois class of L functions" in the following way: $A$ is a Galois class of L functions if and only if the follwing three conditions hold simultaneously: …

In "Lectures on gauge theory and integrable systems" of M.Audin, she identifies the space of conections $\mathcal{A}$ on the trivial bundle $G\times S$ ($G$ Lie group, $S$ surface …

$M$ is a finitely generated $A$-module of dimension $d$ such that $G(M)$ is eqidimensional and $M$ does not have any embedded prime. Given $x\in I$ where $I$ is an ideal of $A$ an …

For an $n$-dimensional orientable closed manifold $M$, the simplicial volume is the infimum of the $l^1$-norm of the elements $\sum a_i \sigma_i$ ($a_i \in \mathbb{R}$) which repre …

Let $M$ be a compact spin$^c$ manifold, so that it has a fundamental class $[M] \in K_n(M)$. It is well-known that the cap product with $[M]$ induces Poincare duality isomorphisms …

Let $\Gamma\subseteq \Gamma'\subset SL_2(\mathbb Z)$ be congruence subgroups, and $X(\Gamma)$, $X(\Gamma')$ be the associated smooth projective modular curves over $\mathbb C$. Th …

This is a somewhat imprecise question, as I am not sure how exactly how to formalise how to do mathematics "without" a certain key tool, but hopefully the intent of the question wi …

It is commonplace to consider applications of mathematics to other fields, especially the exact sciences. But what I would like to know about is the converse topic, namely: Wha …

What invariants of a matrix determine the Smith Normal Form (SNF) of all the powers of a matrix? The question makes sense over any PID $R$. If we let $M = M_n(R)$ and $G=Gl_n(R …