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On Moduli Spaces and CW Structures Arising from Morse Theory On Hilbert Manifolds
Morse theory negative gradient dynamics Hilbert manifold
2011/2/21
This paper proves some results on negative gradient dynamics of Morse functions on Hilbert manifolds. It contains the compactness of ow lines, manifold structures of certain compacti-
ed moduli spa...
This short text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists. I ...
Dilation theory in finite dimensions: the possible, the impossible and the unknown
Dilation theory finite dimensions
2011/2/24
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting a...
Chip-Firing and Riemann-Roch Theory for Directed Graphs
Chip-Firing Riemann-Roch Theory Directed Graphs
2011/1/17
We investigate Riemann-Roch theory for directed graphs. The Riemann-Roch criteria of Amini and
Manjunath is generalized to all integer lattices orthogonal to some positive vector. Using a generalized...
We give a short tour through major parts of a recent long paper [IKR1] on supertropical valuation theory, leaving aside nearly all proofs (to be found in [IKR1]). In this way we hope to give easy acce...
We investigate the relations in Galois groups of maximal p-extensions of fields, the structure of their natural filtrations,and their relationship with the Bloch-Kato conjecture proved by
Rost and Vo...