# Parametrized homotopy theory

@inproceedings{May2006ParametrizedHT, title={Parametrized homotopy theory}, author={Jon P. May and J. Sigurdsson}, year={2006} }

Prologue Point-set topology, change functors, and proper actions: Introduction to Part I The point-set topology of parametrized spaces Change functors and compatibility relations Proper actions, equivariant bundles and fibrations Model categories and parametrized spaces: Introduction to Part II Topologically bicomplete model categories Well-grounded topological model categories The $qf$-model structure on $\mathcal{K}_B$ Equivariant $qf$-type model structures Ex-fibrations and ex…

## 24 Citations

Combinatorial parametrised spectra

- Mathematics
- 2019

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…

A symmetric monoidal and equivariant Segal infinite loop space machine

- MathematicsJournal of Pure and Applied Algebra
- 2019

Generalized String Topology and Derived Koszul Duality

- Mathematics
- 2013

The generalized string topology construction of Gruher and Salvatore assigns to any bundle of $E_n$-algebras $A$ over a closed oriented manifold $M$ a collection of intersection-type operations on…

Homotopical Algebra in Categories with Enough Projectives

- Mathematics
- 2017

For a complete and cocomplete category $\mathcal{C}$ with a well-behaved class of `projectives' $\bar{\mathcal{P}}$, we construct a model structure on the category $s\mathcal{C}$ of simplicial…

The tangent bundle of a model category

- Mathematics
- 2018

This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category $\mathcal{M}$ satisfying suitable…

Strict algebraic models for rational parametrised spectra, I

- Mathematics
- 2020

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…

Equivariant $A$-theory

- Mathematics
- 2016

We give a new construction of the equivariant $K$-theory of group actions (cf. Barwick et al.), producing an infinite loop $G$-space for each Waldhausen category with $G$-action, for a finite group…

Homotopy automorphisms of R-module bundles, and the K-theory of string topology

- Mathematics
- 2013

Let R be a ring spectrum and $$ \mathcal {E}\rightarrow X$$E→X an R-module bundle of rank n. Our main result is to identify the homotopy type of the group-like monoid of homotopy automorphisms of…

Classifying theory for simplicial parametrized groups

- Mathematics
- 2012

In this paper we describe a classifying theory for families of simplicial topological groups. If $B$ is a topological space and $G$ is a simplicial topological group, then we can consider the…

Gauge theory and string topology

- Mathematics
- 2013

Given a principal bundle over a closed manifold, $$G \rightarrow P \rightarrow M$$G→P→M, let $$P^{Ad} \rightarrow M$$PAd→M be the associated adjoint bundle. Gruher and Salvatore (Proc Lond Math Soc…