# 4Manifolds and topological modular forms

The existence of quantum field theories in higher dimensions leads to many interesting predictions in mathematics. Sergei Gukov, Pavel Putrov and Cumrun Vafa). Identities for Poincaré polynomials via. On manifolds with rational string structure the Witten genus takes values.

In mathematics, topological modular forms (tmf) is the name of a spectrum that describes a. Pontryagin class a modular form. We build a connection between topology of smooth 4 – manifolds and the theory of topological modular forms by considering topologically. A historical overview of elliptic cohomology. The motivating reason for the development of topological modular forms. The Donaldson invariants of a smooth simply connected 4 – manifold X depend. Polynomial invariants for smooth four – manifolds, Topology. The theory of topological modular forms is an intricate blend of classical algebraic. It has applications to and connections with manifold topology, number theory, and string theory.

Parameterizing p-complete Orientations. E∞- genera on String manifolds valued in topological modular forms. We construct the Witten orientation of the topological modular forms spectrum. Here, SR is the Moore spectrum associated to the ring R. Geometric cobordism, Milnor manifolds and multiplicativity. There is a rick mathematical structure attached to the cobordism invariants of manifolds. Central problem in algebraic topology: compute π i. Here, tmf denotes the connective spectrum of topological modular forms of. They can be made into framed manifolds using the left invariant framing, and in. The algebraic theory of modular forms Let C be the projective.

Göttsche, “ Modular forms and Donaldson invariants for 4 – manifolds with b1 = 1. Shatashvili, “Issues in topological gauge. Singer index theorem to the case in which a compact topological group G acts on X. Smooth 4 – manifolds and symplectic topology. One then finds easily that and € are modular forms of weights 2 and 4. GMT 4 – manifolds and topological modular forms – arxiv. Witten wrote down a rich ring homomorphism.

Gauge Theory and Four — Manifold Topology, Proc. Göttsche, Modular forms and Donaldson invariants for manifolds with bt = 1. The functions ✏(⌧) and (⌧) are modular forms, of weight 2 and 4 respectively. Consider a smooth 4 – manifold X with Chern characters c1 = 0, c2 = k. Upshot: n even ⇒ bp gives no exotic spheres. Topological string theory and modular forms.

Elliptic Functions and Modular Forms. Stability and Kahler-Einstein Geometry. This workshop will bring experts from the fields of topology, physics and number. Mock Modular Forms and 3- Manifolds – Francesca Ferrari, SISSA. Download Book Manifolds And Modular Forms in PDF format. Fusion 2-categories and a state-sum invariant for 4 – manifolds.

Conformal nets IV: the 3-category.