A product theorem for $H$-group fibrations

A Measurable Stability Theorem for Holomorphic Foliations Transverse to Fibrations

THE h-PRINCIPLE FOR BROKEN LEFSCHETZ FIBRATIONS

It is known that an arbitrary smooth, oriented 4-manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken fibration, there are certain modifications, realized as homotopies of the fibration map, that enable one to construct infinitely many distinct fibrations of the same manifold. The aim of this paper is to prove that these modifications are sufficient to ob...

An Approximation Theorem for Maps into Kan Fibrations

This theorem has an interesting special case. Take X = E a Kan set, Y = S\E\, B a point, p, h the unique constant maps, / = idEf i the natural inclusion and g the natural retraction. What comes out is the famous Milnor-Lamotke theorem saying E is strong deformation retract of S\E\. Thus we get a new proof of this theorem which in contrast to the original one [4] avoids any reference to J.H.C. W...

Factorization systems and fibrations: Toward a fibred Birkhoff variety theorem

It is well-known that a factorization system on a category (with sufficient pullbacks) gives rise to a fibration. This paper characterizes the fibrations that arise in such a way, by making precise the logical structure that is given by factorization systems. The underlying motivation is to obtain general Birkhoff results in a fibred setting.

Theorem Proving for Product Lines

Mechanized proof assistants are powerful verification tools, but proof developments can still be difficult and timeconsuming. When verifying a family of related programs, the effort can be reduced by proof reuse. In this paper, we show how to engineer proofs for product lines built from feature modules. Each module contains proof fragments which are composed together to build a complete proof o...