Tools

LEADER 03585nam 2200505 i 4500

001 ssj0002680114;

003 WaSeSS;

005 20250112080401.0;

006 m d ;

007 cr n ;

008 220713s2022 riu sb 000 0 eng d;

010 a| 2022023089;

020 a| 9781470452698q| (paperback);

020 z| 9781470470968q| (pdf);

035 a| (WaSeSS)ssj0002680114;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QC174.45b| .D44 2022;

082 00 a| 530.14/32| 23/eng20220913;

084 a| 57R56a| 18D102| msc;

100 1 a| De Renzi, Marco,d| 1988-?| UNAUTHORIZED;

245 10 a| Non-semisimple extended topological quantum field theoriesh| [electronic resource] /c| Marco De Renzi.;

260 a| Providence, RI :b| American Mathematical Society,c| 2022.;

300 a| xi, 161 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 277, Number 1364 (fifth of 6 numbers);

504 a| Includes bibliographical references (pages 159-161).;

506 a| Available only to authorized users.;

520 a| "We develop the general theory for the construction of Extended Topological Quantum Field Theories (ETQFTs) associated with the Costantino-Geer-Patureau quantum invariants of closed 3-manifolds. In order to do so, we introduce relative modular categories, a class of ribbon categories which are modeled on representations of unrolled quantum groups, and which can be thought of as a non-semisimple analogue to modular categories. Our approach exploits a 2-categorical version of the universal construction introduced by Blanchet, Habegger, Masbaum, and Vogel. The 1+1+1-EQFTs thus obtained are realized by symmetric monoidal 2-functors which are defined over non-rigid 2-categories of admissible cobordisms decorated with colored ribbon graphs and cohomology classes, and which take values in 2- categories of complete graded linear categories. In particular, our construction extends the family of graded 2+1-TQFTs defined for the unrolled version of quantum sl2 by Blanchet, Costantino, Geer, and Patureau to a new family of graded ETQFTs. The non-semisimplicity of the theory is witnessed by the presence of non-semisimple graded linear categories associated with critical 1-manifolds"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Quantum field theory.=| ^A50511;

650 0 a| Mathematical physics.=| ^A15920;

650 0 a| Topological manifolds.=| ^A134355;

650 7 a| Manifolds and cell complexes -- Differential topology -- Topological quantum field theories.2| msc;

650 7 a| Category theory; homological algebra -- Categories with structure -- Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories.2| msc;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=29731918;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

949 a| CLICK ON WEB ADDRESSw| ASISh| HSL77;

949 a| CLICK ON WEB ADDRESSw| ASISh| JMUSIC60;

596 a| 1 3 4;

998 a| 6515248;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6515248-1001l| JNETm| JOYNERr| Ys| Yt| JNESSBKu| 1/14/2025x| EBOOKz| JERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6515248-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 1/14/2025x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6515248-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/14/2025x| EBOOKz| JERESOURCE;

Non-semisimple extended topological quantum field theories / Marco De Renzi.

Author/creator	De Renzi, Marco, 1988-
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2022.
Description	xi, 161 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Quantum field theory. Mathematical physics. Topological manifolds.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 277, Number 1364 (fifth of 6 numbers)
Abstract	"We develop the general theory for the construction of Extended Topological Quantum Field Theories (ETQFTs) associated with the Costantino-Geer-Patureau quantum invariants of closed 3-manifolds. In order to do so, we introduce relative modular categories, a class of ribbon categories which are modeled on representations of unrolled quantum groups, and which can be thought of as a non-semisimple analogue to modular categories. Our approach exploits a 2-categorical version of the universal construction introduced by Blanchet, Habegger, Masbaum, and Vogel. The 1+1+1-EQFTs thus obtained are realized by symmetric monoidal 2-functors which are defined over non-rigid 2-categories of admissible cobordisms decorated with colored ribbon graphs and cohomology classes, and which take values in 2- categories of complete graded linear categories. In particular, our construction extends the family of graded 2+1-TQFTs defined for the unrolled version of quantum sl2 by Blanchet, Costantino, Geer, and Patureau to a new family of graded ETQFTs. The non-semisimplicity of the theory is witnessed by the presence of non-semisimple graded linear categories associated with critical 1-manifolds"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 159-161).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022023089
ISBN	9781470452698 (paperback)
ISBN	(pdf)

Availability

Library	Location	Call Number	Status	Item Actions
	Electronic Resources	Access Content Online	✔ Available

Non-semisimple extended topological quantum field theories / Marco De Renzi.

Click here for more information about this title

Availability