MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am studying a paper of L. Lovász, ``A homology theory for spanning trees of a graph,'' but professor Babai has told me that Lovász later realized that this work is better framed in the language of homotopy theory.

Does anyone know if Lovász (or anyone else) published a homotopy-based treatment of the results in the above paper?

share|cite|improve this question

I think that this has something to do with what's called A-homotopy theory. In fact, the following two papers on A-homotopy theory reference Lovasz's paper, and from looking at the first paper below it seems like it's exactly the sort of thing you're looking for.

MR1808443 (2001k:57029) Barcelo, Hélène; Kramer, Xenia; Laubenbacher, Reinhard; Weaver, Christopher Foundations of a connectivity theory for simplicial complexes. Adv. in Appl. Math. 26 (2001), no. 2, 97–128. (Reviewer: Andrew Vince), 57Q05 (05B35 05C10 55P99 55Q05)

MR2163440 (2006f:52017) Barcelo, Hélène; Laubenbacher, Reinhard Perspectives on $A$-homotopy theory and its applications. Discrete Math. 298 (2005), no. 1-3, 39–61. (Reviewer: Jean-Louis Cathelineau), 52B40 (05B35 05E25 37F20 52C35 55R80 57Q05)

share|cite|improve this answer
Thanks for the suggested reading! I'll decide whether to accept your answer once I take a careful look. The papers certainly look relevant! – John Wiltshire-Gordon Nov 10 '10 at 4:01

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.