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K-Theory and Homology

New submissions

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New submissions for Tue, 20 Mar 18

[1]  arXiv:1803.06755 [pdf, ps, other]
Title: Witt groups of abelian categories and perverse sheaves
Authors: Jörg Schürmann (Universität Münster), Jon Woolf (University of Liverpool)
Comments: 35 pages
Subjects: Algebraic Topology (math.AT); Algebraic Geometry (math.AG); K-Theory and Homology (math.KT)

In this paper we study the Witt groups of symmetric and anti-symmetric forms on perverse sheaves on a finite-dimensional topologically stratified space with even dimensional strata. We show that the Witt group has a canonical decomposition as a direct sum of the Witt groups of shifted local systems on strata. We compare this with another `splitting decomposition' for Witt classes of perverse sheaves obtained inductively from our main new tool, a `splitting relation' which is a generalisation of isotropic reduction.
The Witt groups we study are identified with the (non-trivial) Balmer-Witt groups of the constructible derived category of sheaves on the stratified space, and also with the corresponding cobordism groups defined by Youssin.
Our methods are primarily algebraic and apply more widely. The general context in which we work is that of a triangulated category with duality, equipped with a self-dual t-structure with noetherian heart, glued from self-dual t-structures on a thick subcategory and its quotient.

[2]  arXiv:1803.06956 [pdf, ps, other]
Title: On a question of Swan
Authors: Dorin Popescu
Subjects: Commutative Algebra (math.AC); Algebraic Geometry (math.AG); K-Theory and Homology (math.KT)

We show that a regular local ring is a filtered inductive limit of regular local rings, essentially of finite type over $\bf Z$.

Replacements for Tue, 20 Mar 18

[3]  arXiv:1409.6943 (replaced) [pdf, ps, other]
Title: Koszul duality between $E_n$-algebras and coalgebras in a filtered category
Authors: Takuo Matsuoka
Comments: Was previously part of arXiv:1312.2562. 35 pages. Technical improvements, more descriptive terminology
Subjects: Algebraic Topology (math.AT); K-Theory and Homology (math.KT)
[4]  arXiv:1611.09680 (replaced) [pdf, ps, other]
Title: Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
Authors: Shin Hayashi
Comments: v3: section 4 added, references and typos corrected. 15 pages, 1 figure
Subjects: Mathematical Physics (math-ph); K-Theory and Homology (math.KT)
[ total of 4 entries: 1-4 ]
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