## Algebraic Topology: Applications and New Directions (Google eBook)Ulrike Tillmann, Søren Galatius, Dev Sinha This volume contains the proceedings of the Stanford Symposium on Algebraic Topology: Applications and New Directions, held from July 23-27, 2012, at Stanford University, Stanford, California. The symposium was held in honor of Gunnar Carlsson, Ralph Cohen and Ib Madsen, who celebrated their 60th and 70th birthdays that year. It showcased current research in Algebraic Topology reflecting the celebrants' broad interests and profound influence on the subject. The topics varied broadly from stable equivariant homotopy theory to persistent homology and application in data analysis, covering topological aspects of quantum physics such as string topology and geometric quantization, examining homology stability in algebraic and geometric contexts, including algebraic img style="width:15px;height:11px" src="http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/004B.png?rev=2.4-beta-2" -theory and the theory of operads. |

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### Contents

1 | |

A stability conjecture for the unstable cohomology of _ ℤ mapping class groups and _ | 55 |

The BoardmanVogt tensor product of operadic bimodules | 71 |

Detecting and realising characteristic classes of manifold bundles | 99 |

Controlled Algebraic theory II | 111 |

More examples of discrete cocompact group actions | 133 |

On the theory of planar cuspical curves and a new family of polytopes | 145 |

Equivariant multiplicative closure | 183 |

a survey | 201 |

The definition of a noncommutative toric variety | 223 |

The Stable Symplectic Category and Quantization | 251 |

A geometric perspective on quantum field theory | 281 |

a survey of persistent homology and its algebraic foundations | 295 |

Cartiers first theorem for Witt vectors on ℤ_0ⁿ0 | 321 |