MathOverflow

I've been considering a research topic based on extending the material from Khoi's research paper concerning a Chern–Simons-type invariant for 3-manifolds, and I'm stuck on a specific problem described below.
In the referenced paper, it is stated that the homology sphere $\Sigma(2, 3, 7)$ carries the $\widetilde{\operatorname{SL}(2, \mathbb{R})}$ geometry so that its volume is $\frac{2\pi^2}{21}$ according to the expression $$ \frac{4\pi^2 \chi(M \longrightarrow...

Let $P,Q$ be two real orthogonal projections on $\mathbb R^n$, and assume that they are permutation similar. More specifically, assume that each of them is permutation similar to a block diagonal matrix of the form
$$\operatorname{diag}\!\left(\frac1m J_m,\frac1m J_m,\dots,\frac1m J_m\right).$$...

A. Neeman has defined K-well generated triangulated categories for any infinite regular cardinal K; in the case $K=\aleph_0$ these are the compactly generated ones. He (and also H. Krause) has also established several nice properties for this definition...

Let $\mathcal{W}$ denote the space of all bounded symmetric measurable functions$W : [0, 1]^2 \rightarrow \mathbb{R}.$ For any $W\in\mathcal{W}$ we say it is a kernel and define its cut norm $\lVert W\rVert_\square=\sup\limits_{S,T\subseteq [0,1]}\Big...