# Strict algebraic models for rational parametrised spectra, I

@article{BraunackMayer2019StrictAM, title={Strict algebraic models for rational parametrised spectra, I}, author={Vincent Braunack-Mayer}, journal={arXiv: Algebraic Topology}, year={2019} }

In this article, we extend Sullivan's PL de Rham theory to obtain simple algebraic models for the rational homotopy theory of parametrised spectra. This simplifies and complements the results of arXiv:1910.14608, which are based on Quillen's rational homotopy theory.
According to Sullivan, the rational homotopy type of a nilpotent space $X$ with finite Betti numbers is completely determined by a commutative differential graded algebra $A$ modelling the cup product on rational cohomology. In…

## 4 Citations

### Combinatorial parametrised spectra

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We obtain combinatorial model categories of parametrised spectra, together with systems of base change Quillen adjunctions associated to maps of parameter spaces. We work with simplicial objects and…

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### A T ] 1 9 Ju l 2 01 9 Combinatorial parametrised spectra

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We obtain combinatorial model categories of parametrised spectra, together with systems of base change Quillen adjunctions associated to maps of parameter spaces. We work with simplicial objects and…

### Gauge Enhancement of Super M-Branes Via Parametrized Stable Homotopy Theory

- MathematicsCommunications in Mathematical Physics
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AbstractA key open problem in M-theory is to explain the mechanism of “gauge enhancement” through which M-branes exhibit the nonabelian gauge degrees of freedom seen perturbatively in the limit of…

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We obtain combinatorial model categories of parametrised spectra, together with systems of base change Quillen adjunctions associated to maps of parameter spaces. We work with simplicial objects and…

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