8 papers
Transport functions for principal bundles and Morse homology with differential graded coefficients
Maximilian Stegemeyer
We study transport functions as a Morse-theoretical way of describing principal bundles. Transport functions are maps from the spaces of broken gradient flow lines to a topological…
String topology coproduct and Turaev cobracket on surfaces
Jana Hartenstein, Maximilian Stegemeyer
The string topology coproduct on the homology of the free loop space of a closed manifold induces a string cobracket on -equivariant homology. We give a complete computation o…
Extensions of the loop product and coproduct, the space of antipodal paths and resonances of closed geodesics
Maximilian Stegemeyer
We study the space of paths in a closed manifold with endpoints determined by an involution . If the involution is fixed point free and if is -connected…
Intersection Multiplicity in Loop Spaces and the String Topology Coproduct
Philippe Kupper, Maximilian Stegemeyer
The string topology coproduct is often perceived as a counterpart in string topology to the Chas-Sullivan product. However, in certain aspects the string topology coproduct is much…
String topology on the space of paths with endpoints in a submanifold
Maximilian Stegemeyer
In this article we consider algebraic structures on the homology of the space of paths in a manifold with endpoints in a submanifold. The Pontryagin-Chas-Sullivan product on the ho…
On the string topology of symmetric spaces of higher rank
Philippe Kupper, Maximilian Stegemeyer
The homology of the free and the based loop space of a compact globally symmetric space can be studied through explicit cycles. We use cycles constructed by Bott and Samelson and b…
The string topology coproduct on complex and quaternionic projective space
Maximilian Stegemeyer
On the free loop space of compact symmetric spaces Ziller introduced explicit cycles generating the homology of the free loop space. We use these explicit cycles to compute the str…
On the String Topology Coproduct for Lie Groups
Maximilian Stegemeyer
The free loop space of a Lie group is homeomorphic to the product of the Lie group itself and its based loop space. We show that the coproduct on the homology of the free loop spac…