Short and simple: given an element $x$ in the cobar complex for $BP_* BP$, this program computes the coboundary $\mathrm{d}x$. For example: fire up the program and enter

v2 [t1^2 t2 | t3] + v3

and you should see:

-16 [ t1^7 ]
 + -4 [ t1t2^2 ]
 + 2 [ t3 ]
 + -56 v1 [ t1^6 ]
 + -1 v1 [ t2^2 ]
 + ... <61 more lines>

This program was written very quickly during collaborative computation sessions with Michael Andrews. It’s not at all a polished program at this stage. If there are features or refinements that would be useful to see here, get in touch!

This software is open-source, hosted in this github repository.

How to use

Running the program requires only a single jar file, available here.

You’ll want to run it from the command-line, e.g. by

java -jar bpcobar-latest.jar


This repository includes a shell script make for compiling. Currently it’s a bit specialized to my machine, in particular referring to a Java 6 runtime rt.jar in a subfolder, but it shouldn’t be too hard to get it built if you’re into Java. Feel free to contact me.