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Working notes for "Constructing A-infinity categories of matrix factorisations"
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working-ainfmf.md

Constructing A-infinity categories of matrix factorisations

I am making publicly available my hand-written working notes for the paper "Constructing A-infinity categories of matrix factorisations" in the same spirit that I made available the other notes on my webpage The Rising Sea. Obviously you should not expect these notes to be as coherent, or readable, as the final paper, but those marked on the first page as (checked) are indeed checked, to the same level of rigour that I apply to any of my published papers. And they often contain more details than the paper. I hope you find them useful!

Notes directly used in writing the paper

The main references, written in the same notation and from the same outlook as the final paper, are given below. You should probably start with (ainfmf28). Some of these PDF files are large, you have been warned.

  • (ainfmf28), (ainfmf29) are the basis for Section 3 and Appendix B of the paper.
  • (ainfmf30) Koszul matrix factorisations (Section 5.1 of the paper)
  • (ainfmf33) On formal tubular neighborhoods (Appendix A of the paper)
  • (ainfmf34) Removing Noetherian hypotheses (Appendix C of the paper)
  • (ainfcat), (ainfcat2), (ainfcat3) are my notes on the basic theory of A-infinity categories following Lazaroiu's paper including a detailed proof of the minimal model theorem and an analysis of various different possible conventions for operator decorated trees (includes Appendix D of the paper).

Many of the important aspects of the construction were discussed at a mini-course on A-infinity categories and matrix factorisations, September 2017 at the IBS in Korea (lecture 1, lecture 2, lecture 3).

In case you're wondering, the newer notes here were written using an iPad Pro and Goodnotes.

Older or less important notes

My initial notes are focused on the case of the endomorphism DG-algebra of the generator, and contain some calculations in special cases. However the notation and setup have changed a bit between these old notes and the paper, so YMMV. The first place to look is probably (ainfmf12) and then follow the links there to older notes if necessary. (ainfmf9),(ainfmf2) might also be useful, the rest is probably not.

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