Given a manifold X, the ordered configuration space of n points in X, denoted F_{n}(X), is the space of ways of putting n labeled non-overlapping points in X. Church--Ellenberg--Farb showed that if X is a connected non-compact orientable finite type manifold of dimension d at least 2, then (H_{k}(F_{n}(X)))_{n} stabilizes as a sequence of symmetric group representations. Miller--Wilson extended this first-order representation stability to non-orientable manifolds, and proved that there is a stability pattern among the unstable terms of the sequence. In this thesis we prove that there exists a manifold such that this secondary stability sequence is neither free nor stably-zero, providing the first example of such a phenomenon. In the second...
We introduce ordered and unordered configuration spaces of 'clusters' ofpoints in an Euclidean space...
This thesis sets out to explore and implement the paradigm of representation stability, specifically...
© 2015 Dr. Jeffrey Steven BailesThe heart of this thesis tries to extend previous ideas about homolo...
We consider the ordered configuration space of $n$ open unit-diameter disks in the infinite strip of...
In this thesis we study the homological behaviour of configuration spaces as the number of objects i...
We study the homology of ordered configuration spaces and Deligne--Mumford compactifications using t...
We study stability patterns in the high dimensional rational homology of unordered configuration spa...
Secondary homological stability is a recently discovered stability pattern for the homology of a seq...
Abstract. We introduce new maps between configuration spaces of points in a background manifold, the...
We give $\mathbb{Z}$-bases for the homology and cohomology of the configuration space $\operatorname...
The generalized configuration spaces are the different fat sub-diagonals of the cartesian product of...
In this paper we decompose the rational homology of the ordered configuration space of $p$ open unit...
Abstract. We prove that the dual rational homotopy groups of the configuration spaces of a 1-connect...
© 2014 Dr. TriThang TranThis thesis has two purposes. The first is to serve as an introductory surve...
We give a definition of the scanning map for configuration spaces that is equivariant under the acti...
We introduce ordered and unordered configuration spaces of 'clusters' ofpoints in an Euclidean space...
This thesis sets out to explore and implement the paradigm of representation stability, specifically...
© 2015 Dr. Jeffrey Steven BailesThe heart of this thesis tries to extend previous ideas about homolo...
We consider the ordered configuration space of $n$ open unit-diameter disks in the infinite strip of...
In this thesis we study the homological behaviour of configuration spaces as the number of objects i...
We study the homology of ordered configuration spaces and Deligne--Mumford compactifications using t...
We study stability patterns in the high dimensional rational homology of unordered configuration spa...
Secondary homological stability is a recently discovered stability pattern for the homology of a seq...
Abstract. We introduce new maps between configuration spaces of points in a background manifold, the...
We give $\mathbb{Z}$-bases for the homology and cohomology of the configuration space $\operatorname...
The generalized configuration spaces are the different fat sub-diagonals of the cartesian product of...
In this paper we decompose the rational homology of the ordered configuration space of $p$ open unit...
Abstract. We prove that the dual rational homotopy groups of the configuration spaces of a 1-connect...
© 2014 Dr. TriThang TranThis thesis has two purposes. The first is to serve as an introductory surve...
We give a definition of the scanning map for configuration spaces that is equivariant under the acti...
We introduce ordered and unordered configuration spaces of 'clusters' ofpoints in an Euclidean space...
This thesis sets out to explore and implement the paradigm of representation stability, specifically...
© 2015 Dr. Jeffrey Steven BailesThe heart of this thesis tries to extend previous ideas about homolo...