Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs
Gukov-Pei-Putrov-Vafa constructed q-series invariants called homological blocks in a physical way to categorify Witten-Reshetikhin-Turaev (WRT) invariants and conjectured that radial limits of homological blocks are WRT invariants. In this paper, we prove their conjecture for unimodular H-graphs. As...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2022 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2022
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211634 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs. Akihito Mori and Yuya Murakami. SIGMA 18 (2022), 034, 20 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862744649235431424 |
|---|---|
| author | Mori, Akihito Murakami, Yuya |
| author_facet | Mori, Akihito Murakami, Yuya |
| citation_txt | Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs. Akihito Mori and Yuya Murakami. SIGMA 18 (2022), 034, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Gukov-Pei-Putrov-Vafa constructed q-series invariants called homological blocks in a physical way to categorify Witten-Reshetikhin-Turaev (WRT) invariants and conjectured that radial limits of homological blocks are WRT invariants. In this paper, we prove their conjecture for unimodular H-graphs. As a consequence, it turns out that the WRT invariants of H-graphs yield quantum modular forms of depth two and of weight one with the quantum set ℚ. In the course of the proof of our main theorem, we first write the invariants as finite sums of rational functions. We secondly carry out a systematic study of weighted Gauss sums in order to give new vanishing results for them. Combining these results, we finally prove that the above conjecture holds for H-graphs.
|
| first_indexed | 2026-04-17T18:48:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211634 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T18:48:49Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Mori, Akihito Murakami, Yuya 2026-01-07T13:42:30Z 2022 Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs. Akihito Mori and Yuya Murakami. SIGMA 18 (2022), 034, 20 pages 1815-0659 2020 Mathematics Subject Classification: 57K31; 57K10; 57K16; 11F27; 11L05; 11T24 arXiv:2110.10958 https://nasplib.isofts.kiev.ua/handle/123456789/211634 https://doi.org/10.3842/SIGMA.2022.034 Gukov-Pei-Putrov-Vafa constructed q-series invariants called homological blocks in a physical way to categorify Witten-Reshetikhin-Turaev (WRT) invariants and conjectured that radial limits of homological blocks are WRT invariants. In this paper, we prove their conjecture for unimodular H-graphs. As a consequence, it turns out that the WRT invariants of H-graphs yield quantum modular forms of depth two and of weight one with the quantum set ℚ. In the course of the proof of our main theorem, we first write the invariants as finite sums of rational functions. We secondly carry out a systematic study of weighted Gauss sums in order to give new vanishing results for them. Combining these results, we finally prove that the above conjecture holds for H-graphs. The first and second authors are supported by JSPS KAKENHI Grant Numbers JP 21J10271 and 20J20308. The first author was supported by a Scholarship of Tohoku University, Division for Interdisciplinary Advanced Research and Education. We would like to show our greatest appreciation to Professor Yuji Terashima and Takuya Yamauchi for giving many pieces of advice. Wearedeeply grateful to Professor Kazuhiro Hikami for giving many comments. The first author thanks his family for all the support. We thank the referees for helpful suggestions and comments, which substantially improved the presentation of our paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs Article published earlier |
| spellingShingle | Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs Mori, Akihito Murakami, Yuya |
| title | Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs |
| title_full | Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs |
| title_fullStr | Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs |
| title_full_unstemmed | Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs |
| title_short | Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs |
| title_sort | witten-reshetikhin-turaev invariants, homological blocks, and quantum modular forms for unimodular plumbing h-graphs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211634 |
| work_keys_str_mv | AT moriakihito wittenreshetikhinturaevinvariantshomologicalblocksandquantummodularformsforunimodularplumbinghgraphs AT murakamiyuya wittenreshetikhinturaevinvariantshomologicalblocksandquantummodularformsforunimodularplumbinghgraphs |