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In mathematics, topological modular forms (tmf) is the name of a spectrum that describes a generalized cohomology theory. In concrete terms, for any integer...

spectra. This was later used in the Hopkins–Miller construction of topological modular forms. Subsequent work of Hopkins on this topic includes papers on the...

equation with respect to the group action of the modular group, and a growth condition. The theory of modular forms therefore belongs to complex analysis. The...

topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular...

ring π*(tmf) is called the ring of topological modular forms. TMF is tmf with the 24th power of the modular form Δ inverted, and has period 242=576....

Awards TMF Group, a Dutch multinational in the accounting industry Topological modular forms, an E-infinity ring spectrum used in algebraic topology Tour du...

In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of...

; Francis, John; Henriques, André G; Hill, Michael A. (eds.). Topological modular forms (PDF). Providence, Rhode Island. ISBN 978-1-4704-1884-7. OCLC 884782304...

In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time...

Topological game Topological graph theory Topological K-theory Topological modular forms Topological skeleton Topology optimization Water, gas, and electricity...

physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order...

of the modular group, with these sitting as lattices inside the (topological) universal covering group SL2(R) → PSL2(R). Further, the modular group has...

fundamental objects in the classical theory of modular forms; the modern theory of automorphic forms makes a similar use of congruence subgroups in more...

processors, the first used a toric code with twist defects as a topological degenerancy (or topological defect) while the second used a different but related protocol...

lattice is the underlying object with which elliptic functions and modular forms are defined. A fundamental pair of periods is a pair of complex numbers...

invariant under such deformations is a topological property. The following are basic examples of topological properties: the dimension, which allows...

\in \mathbb {H} } g 2 , g 3 {\displaystyle g_{2},g_{3}} are so called modular forms. The Fourier series for g 2 {\displaystyle g_{2}} and g 3 {\displaystyle...

Niko (2014-12-01). "Secondary invariants for string bordism and topological modular forms". Bulletin des Sciences Mathématiques. 138 (8): 912–970. doi:10...

 R) / {±I}, where I denotes the 2 × 2 identity matrix. It contains the modular group PSL(2, Z). Also closely related is the 2-fold covering group, Mp(2...

graphs, or general topological spaces like simplicial complexes and CW complexes. TDL addresses this by incorporating topological concepts to process...