# Homological Stability for Spaces of Subsurfaces with Tangential Structure

@article{Kastenholz2018HomologicalSF, title={Homological Stability for Spaces of Subsurfaces with Tangential Structure}, author={Thorben Kastenholz}, journal={arXiv: Algebraic Topology}, year={2018} }

Given a closed, simply connected and at least $5$-dimensional manifold $M$ together with some $p\in M$ and a two-plane $A$ in $T_pM$, one can consider the space of submanifolds of $M$ that are diffeomorphic to a surface of genus $g$ and that meet $p$ tangential to $A$. We introduce a notion of tangential structure for these subsurfaces and construct a stabilization map for these spaces of subsurfaces which increases the genus by $1$. Then we proceed to prove homological stability for these… Expand

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