Given a spanning set, consider the minimum number of vectors that you must remove in order to make it no longer span. What is this number called? If the vectors are columns in a …

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 $\scr A$ be an abelian category with exact products and a cogenerator (e.g. $\scr A$ is a category of modules). Let ${\mathbf K}(\scr A)$ be the homotopy category of cochain c …

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 …

This question is inspired by Joseph O'Rourke's beautiful answer to my previous question. Let $\mathbb{S}^{d\times n}$ denote the set of real $d\times n$ matrices whose columns hav …

This is a question I asked at Math.SE but got no answers: http://math.stackexchange.com/q/397164/7110/ Atiyah and Hirzebruch showed in their paper "Vector bundles and homogeneous …

I was dealing with a convolution type integral $$ \int^z_0 t^m {}_0F_1(;1;-t) \: {}_2F_3\Big( 1,1;2,m,m+1 ; -a t\Big) \:\mathrm{d}t $$ By applying one of the identities in Exton's …

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 …

I recently started reading about hyperbolic dynamics in the notes of L. Wen, http://www6.cityu.edu.hk/rcms/publications/ln5.pdf and in this (page 8) there is the following s …

Let $M$ be a (discrete) monoid acting on a space $X.$ We may take the quotient of $X,$ by this action, $X/M$ that is the coequalizer of the action map $M \times X \to X$ against th …

A partial permutation matrix $\pi$ is one with at most one 1 in any row and column (the rest 0s). Given one, we can cross out to the East and South (but not Southeast) of each 1. S …

What is a reference for the subject of "free resolutions for Lie algebras"? Does the term "standard resolutions" means "free resolutions"? What is a "bar resolution"? Is there o …

Where in literature can one find a construction of Steenrod reduced powers (for an odd $p$) that (1) works for the singular cohomology of arbitrary topological spaces (or, more …

Dear all, I stumbled on this question due to an application in physics, but I find it hard to find useful references for it. I looked into literature on projective geometry and po …

This problem cropped up in the context of scale-insensitive methods for generating random variables. Let $X=R^n \cup \{\infty\}$. Suppose we consider a set of transforms $\cal{T} …