Topological Modular Forms, the Witten Genus, and the Theorem of the Cube

1995 ◽  
pp. 554-565 ◽  
Author(s):  
Michael J. Hopkins
Keyword(s):  
Modular Forms ◽  
Topological Modular Forms ◽  
Witten Genus

scholarly journals 4-manifolds and topological modular forms

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Sergei Gukov ◽  
Du Pei ◽  
Pavel Putrov ◽  
Cumrun Vafa
Keyword(s):  
Modular Forms ◽  
Flavor Symmetry ◽  
Basic Properties ◽  
Topological Modular Forms ◽  
Witten Genus

Abstract We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0, 1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on ’t Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra.

scholarly journals The Picard group of topological modular forms via descent theory

2016 ◽  
Vol 20 (6) ◽  
pp. 3133-3217 ◽  
Author(s):  
Akhil Mathew ◽  
Vesna Stojanoska
Keyword(s):  
Modular Forms ◽  
Picard Group ◽  
Descent Theory ◽  
Topological Modular Forms

scholarly journals Topological Modular Forms of Level 3

2009 ◽  
Vol 5 (2) ◽  
pp. 853-872 ◽  
Author(s):  
Mark Mahowald ◽  
Charles Rezk
Keyword(s):  
Modular Forms ◽  
Topological Modular Forms ◽  
Level 3

scholarly journals On the ring of cooperations for 2‐primary connective topological modular forms

2019 ◽  
Vol 12 (2) ◽  
pp. 577-657 ◽  
Author(s):  
M. Behrens ◽  
K. Ormsby ◽  
N. Stapleton ◽  
V. Stojanoska
Keyword(s):  
Modular Forms ◽  
Topological Modular Forms

scholarly journals Secondary invariants for string bordism and topological modular forms

2014 ◽  
Vol 138 (8) ◽  
pp. 912-970 ◽  
Author(s):  
Ulrich Bunke ◽  
Niko Naumann
Keyword(s):  
Modular Forms ◽  
Topological Modular Forms

scholarly journals Topological modular forms with level structure

2015 ◽  
Vol 203 (2) ◽  
pp. 359-416 ◽  
Author(s):  
Michael Hill ◽  
Tyler Lawson
Keyword(s):  
Modular Forms ◽  
Level Structure ◽  
Topological Modular Forms
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