 | Jöllenbeck M. Minimal resolutions via algebraic discrete Morse theory / M.Jöllenbeck, V.Welker. - Providence: American Mathematical Society, 2009. - vi, 74 p. - (Memoirs of the American Mathematical Society; Vol.197, N 923). - Bibliogr.: p.71-72. - Ind.: p.73-74. - ISBN 978-0-8218-4257-7; ISSN 0065-9266
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Chapter 1. Introduction ......................................... 1
Chapter 2. Algebraic Discrete Morse Theory ...................... 7
Chapter 3. Resolution of the Residue Field in the Commutative
Case ................................................ 11
1. Gröbner Bases and Discrete Morse Theory .................. 11
2. An Anick Resolution for the Commutative Polynomial
Ring ..................................................... 14
3. Two Special Cases ........................................ 17
Chapter 4. Resolution of the Residue Field in the Non-
Commutative Case .................................... 21
1. Non-commutative Gröbner Bases and Discrete Morse
Theory ................................................... 21
2. The Anick Resolution ..................................... 23
3. The Poincaré-Betti Series of k ........................... 24
4. Examples ................................................. 25
Chapter 5. Application to the Acyclic Hochschild Complex ....... 29
1. Hochschild Homology and Discrete Morse Theory ............ 29
2. Explicit Calculations of Hochschild Homology ............. 31
Chapter 6. Minimal (Cellular) Resolutions for (p-)Borel Fixed
Ideals .............................................. 35
1. Cellular Resolutions ..................................... 35
2. Cellular Minimal Resolution for Principal Borel Fixed
Ideals ................................................... 37
3. Cellular Minimal Resolution for a Class of p-Borel
Fixed Ideals ............................................. 40
Appendix A. The Bar and the Hochschild Complex ................. 57
Appendix B. Proofs for Algebraic Discrete Morse Theory ......... 61
Bibliography ................................................... 71
Index .......................................................... 73
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