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03279aam a2200337 i 4500 001 3AECC4AA072811ED93C2E7E557ECA4DB 003 SILO 005 20220719010102 008 220506t20222022riua b 000 0 eng d 020 $a 9781470452698 020 $a 1470452693 035 $a (OCoLC)1314258997 040 $a YDX $b eng $e rda $c YDX $d UNBCA $d EAU $d PAU $d NUI $d SILO 050 4 $a QA3 $b .A557 no.1364 100 1 $a De Renzi, Marco, $e author 245 10 $a Non-semisimple extended topological quantum field theories / $c Marco De Renzi. 264 1 $a Providence, RI : $b AMS, American Mathematical Society, $c [2022] 300 $a xi, 161 pages : $b illustrations ; $c 26 cm. 490 1 $a Memoirs of the American Mathematical Society, $x 0065-9266 ; $v Number 1364 500 $a "May 2022, volume 277, number 1364 (fifth of 6 numbers)." 504 $a Includes bibliographical references (pages 159-161). 505 0 $a Preface -- Main results -- Where to find a quantum invariant and a TQFT inside an ETQFT -- Outline of the construction -- Structure of the exposition -- Chapter 1. Relative modular categories -- 1.1 Pivotal and ribbon linear categories -- 1.2 Group structures and ribbon graphs -- 1.3 Group actions and group realizations -- 1.4 Projective traces and ambidextrous objects -- 1.5 Relative pre-modular categories -- 1.6 Main definition -- 1.7 Relation with semisimple theory -- Chapter 2. Admissible cobordisms -- 2.1 Group colourings -- 2.2 2-Category of decorated cobordisms -- 2.3 2-Category of admissible cobordisms -- Chapter 3. Extension of Constantino-Geer-Patureau invariants 3.1 Projective and generic stabilizations -- 3.2 Constantino-Geer-Patureau invariants -- 3.3 Universal construction -- 3.4 Extended universal construction -- Chapter 4. Combinatorial and topological properties -- 4.1 Skein equivalence -- 4.2 Surgery axioms -- 4.3 Connection, domination, triviality -- Chapter 5. Graded extensions -- 5.1 2-Spheres -- 5.2 3-Discs -- 5.3 3-Pants -- 5.4 Graded extended universal construction -- Chapter 6. Symmetric monoidality -- 6.1 Graded ETQFT -- 6.2 Graded TQFT -- Chapter 7. Characterization of the image -- 7.1 1-Spheres -- 7.2 2-Discs -- 7.3 2-Pants -- 7.4 2-Cylinders -- 7.5 Examples of computations -- Appendix A. Unrolled quantum groups -- A.1 Even roots of unity -- A.2 Odd roots of unity -- Appendix B. Manifolds and cobordisms with corners -- B.1 Manifolds with corners -- B.2 Collars -- B.3 Gluing -- B.4 Cobordisms with corners -- Appendix C. Signature defects -- C.1 Intersection pairings -- C.2 Lagrangian subspaces -- C.3 Maslov indices -- Appendix D. Symmetric monoidal 2-categories -- D.1 2-Categories -- D.2 Symmetric monoidal structures -- Appendix E. Complete linear and graded linear categories -- E.1 Linear and graded linear categories -- E.2 Complete linear categories -- E.3 Complete graded linear categories -- E.4 Proofs. 650 0 $a Quantum groups. 650 0 $a Algebraic topology. 650 0 $a Topological fields. 650 0 $a Quantum field theory. 773 18 $w 990007620060202771 $g no:31858073069944 830 0 $a Memoirs of the American Mathematical Society ; $v no. 1364. 941 $a 1 952 $l OVUX522 $d 20231117024243.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=3AECC4AA072811ED93C2E7E557ECA4DBInitiate Another SILO Locator Search