Deformation complexes for algebraic operads and their applications [PhD thesis]

✍ Scribed by Brian Paljug

• Publisher: Temple University
• Year: 2015
• Tongue: English
• Leaves: 120
• Category: Library

✦ Table of Contents

DEDICATION......Page 1
List of Figures......Page 9
INTRODUCTION......Page 10
Notation & conventions......Page 15
Operads......Page 17
Homotopy algebras......Page 24
A basis for the operad -2 3942"613A``4547"603AGer......Page 26<br>The dg operad of brace trees......Page 27<br>Basic definition and properties......Page 30<br>Cohomological properties......Page 33<br>Derivations of3942"613A45`47`"603ACyl(C)......Page 40<br>Derived automorphisms of `39`42`"613A4547"603ACyl(C)......Page 45
3942"613A``4547"603ACyl(C) and diagrams of3942"613A45`47`"603ACobar(C)-algebras......Page 48<br>Homotopy uniqueness......Page 52<br>TAMARKIN'S CONSTRUCTION OF FORMALITY MORPHISMS......Page 56<br>ACTIONS OF THE GROTHENDIECK-TEICHMUELLER GROUP ON TAMARKIN'S CONSTRUCTION......Page 63<br>The action of `39`42`"613A4547"603AGRT1 on 0 (to. 3942"613A``4547"603AGer3942"613A45`47`"603ABraces)to.......Page 64<br>The action of `39`42`"613A4547"603AGRT1 on 0 (to. VA C(A) )to.......Page 65
The theorem on 3942"613A``4547"603AGRT1-equivariance......Page 67<br>The proof of Proposition 7.1......Page 70<br>The sets3942"613A45`47`"603ADrAssoc of Drinfeld associators......Page 74<br>A map B from `39`42`"613A4547"603ADrAssoc1 to 0 (to. 3942"613A``4547"603AGer3942"613A45`47`"603ABraces)to.......Page 76<br>REFERENCES......Page 79<br>A LEMMA ON COLIMITS FROM CONNECTED GROUPOIDS......Page 84<br>ON COHOMOLOGOUS DERIVATIONS AND HOMOTOPIC AUTOMORPHISMS......Page 86<br>FILTERED HOMOTOPY LIE ALGEBRAS......Page 91<br>A lemma on adjusting Maurer-Cartan elements......Page 93<br>Convolution -1`39`42`"613A4547"603ALie-algebra, -morphisms and their homotopies......Page 95
TAMARKIN'S RIGIDITY......Page 98
The standard Gerstenhaber structure on VA is ``rigid''......Page 104
The Gerstenhaber algebra VA is intrinsically formal......Page 107
ON DERIVATIONS OF HOMOTOPY DIAGRAMS......Page 117