Introduction
The materia l i n thes e note s represent s Join t wor k wit h Richar d Tolimier i
and was muc h influence d b y m y previou s Join t work wit h Jonatha n Brezin .
In addition, som e o f th e concept s wer e develope d i n a Join t effor t o f myself ,
Tolimieri an d Barr y Kol b tha t wa s announce d i n [7] . I n presenting th e material ,
I have trie d t o la y a carefu l foundation , an d I have stresse d low-dimensiona l
examples an d specia l computation s eve n when I later prov e genera l result s b y
general techniques . Also , th e las t tw o section s ar e minimall y develope d
with th e int e res ted reade r bein g urge d t o consul t Tolimier i [11 ] for a complet e
treatment.
The relatio n o f thes e Note s t o th e classica l literatur e shoul d be self -
evident an d th e result s i n [3 ] will mak e thi s mor e specifi c fo r th e intereste d
reader. However , thes e note s d o somethin g tha t ma y no t be s o evident . I n
three importan t work s [14], [12], [13] A. Wei l present s a proo f o f th e Planchere i
Theorem, a ne w treatmen t o f Abelia n varietie s an d what we no w cal l th e
Weil-Brezin map . Tha t al l thes e ar e inter-relate d i s b y n o mean s apparent .
In these note s the y al l becom e unite d i n th e stud y o f nil-thet a functions .
Acknowledgement
I would lik e t o than k Clevelan d Stat e Universit y fo r actin g a s hos t
Institute an d Professo r Alla n Silberge r fo r hi s effort s tha t mad e th e Regiona l
Meeting suc h a success .
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