Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map

Details Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map

2011-12-09

arxiv.org/abs/1112.2203v1

Mathematics

Algebraic Topology

Scientific paper

We introduce and study a general theory of objects parametrized by spaces, in the setting of infinity categories. This framework specializes to give an infinity categorical model of parametrized spectra, and we apply these foundations to study the multiplicative properties of the generalized Thom spectrum functor. As part of this work we study the Picard space of a presentable monoidal infinity category. We sharpen classical results due to Lewis about the multiplicative properties of the Thom isomorphism. Our main application is the construction of twisted Umkehr maps on twistings of generalized cohomology theories.

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