True Logick is Neohermetic Pythagoreanism for the the modern mathematician.

New entry!

Computational complexity and 3-manifolds and zombies

Article by Greg Kuperberg and Eric Samperton

In collections: Attention-grabbing titles, Basically computer science

We show the problem of counting homomorphisms from the fundamental group of a homology \(3\)-sphere \(M\) to a finite, non-abelian simple...

URL: http://arxiv.org/abs/1707.03811v1

PDF: http://arxiv.org/pdf/1707.03811v1

Entry: http://read.somethingorotherwhatever.com/entry/Computationalcomplexityand3manifoldsandzombies

Like, doing this just feels weird: \( \bigcirc_{i=1}^nf_i := f_1 \circ f_2 \circ \dots \circ f_n \)

Idle thought: with the exception of \( \sum \) and \( \prod \), transforming an associative binary operation into an agglomerative "summation notation" is just making the symbol big and adding sub/superscripts. E.g., \( \bigotimes_{i=0}^n v_i \). It's strange to me that this applies to non-commutative operators ( \( \wedge \) ), but also that there are many binary operations where this rule can't be applied due to limitations of the syntax (bracket operators, function composition, modulo).

I recently learned about Ologs, which are basically "category theory for normal people". These are very useful for knowledge representation. I am now in the making of a blog post about how to make them and how to translate ologs to Haskell code.

http://briss.sourceforge.net/

Let \(Y\) be a subspace of \(X\). The wizard hat space \(W\) is constructed by attaching the base of the cone \(CY\) over \(Y\) to \(X\) along \(Y\).

(This showed up in a topology class I took once. We needed to use the fact that \(W\) deformation retracts onto \(X\), but I don't remember what it was used for. The name is mine.)

University of Illinois at Chicago

Geometric Group Theorist

http://math.uic.edu/~perez

Joined Jun 2017