Rational homotopy theory: a brief introduction

Kathryn Hess

arxiv: math/0604626 · v2 · submitted 2006-04-28 · 🧮 math.AT

Rational homotopy theory: a brief introduction

Kathryn Hess This is my paper

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keywords theorybriefhomotopyintroductionmodelrationalcategorycommutative

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These notes contain a brief introduction to rational homotopy theory: its model category foundations, the Sullivan model and interactions with the theory of local commutative rings.

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Generalised Symmetries and Swampland-Type Constraints from Charge Quantisation via Rational Homotopy Theory
hep-th 2026-04 unverdicted novelty 6.0

Refining charge quantization via a homotopy type A yields swampland-like constraints ruling out noncompact gauge groups and non-nilpotent one-form Lie algebras, and requires A to be contractible for quantum gravity theories.
Generalised Symmetries and Swampland-Type Constraints from Charge Quantisation via Rational Homotopy Theory
hep-th 2026-04 unverdicted novelty 6.0

Refines charge quantization via homotopy type A whose homotopy groups classify brane charges and homology groups classify higher-form symmetries, deriving swampland-like constraints that rule out noncompact gauge grou...