A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study PL bordism theories with quantitative bounds on filling simplices.
The paper classifies certain PL manifolds using PL cobordism.
Solves linearity problem for acyclic groups, bounds Cheeger-Gromov ρ-invariants.
In this paper, we introduce a bordism category whose objects are bundles of closed -dimensional piecewise linear manifolds and whose morphisms are bundles of -dimensional piecewise linear cobordisms. In the main theorem of this article, we show that the classifying space $B\mathcal{C}_d^{…
We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree -1. We prove that there are strongly chiral, smoo…
We study bordism groups and bordism homology theories based on pseudomanifolds and stratified pseudomanifolds. The main seam of the paper demonstrates that when we uses classes of spaces determined by local link properties, the stratified and unstratified bordism theories are identical; this includes the known examples…
New perspective on APS indices preserves orientations and gradings through bordisms.
We call a Morse function on a closed manifold -constrained if neither nor has critical points of indefinite Morse index . In this paper we study bordism groups of -constrained Morse functions, and thus interpolate between the case of bordism groups of Morse functions (computed by Ikegami…
This note provides a computation of the bordism groups of K-Witt spaces for fields K with characteristic 2. We provide a complete computation for the unoriented bordism groups. For the oriented bordism groups, a nearly complete computation is provided as well a discussion of the difficulty of resolving a remaining ambi…
The group of bordism classes of unoriented surfaces in 4-space is determined. The bordism classes are characterized by normal Euler numbers,double linking numbers, and triple linking numbers.
Quantum field theory uses Lorentzian bordisms to describe time evolution.
We introduce characteristics into chromatic homotopy theory. This parallels the prime characteristics in number theory as well as in our earlier work on structured ring spectra and unoriented bordism theory. Here, the K(n)-local Hopkins-Miller classes take the places of the prime numbers, and this allows us to di…
This paper shows that, away from 6, the kernel of the Witten genus is precisely the ideal consisting of (bordism classes of) Cayley plane bundles with connected structure group, but only after restricting the Witten genus to string bordism. It does so by showing that the divisibility properties of Cayley plane bundle c…
We define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the mapping class group. The second and third terms of this filtration are the well-known Torelli group and Johnson subgroup, respectively. We i…
The groups of link bordism can be identified with homotopy groups via the Pontryagin-Thom construction. B.J. Sanderson computed the bordism group of 3 component surface-links using the Hilton-Milnor Theorem, and later gave a geometric interpretation of the groups in terms of intersections of Seifert hypersurfaces and t…
Generalised characteristic classes are constructed for bordism cohomologies which allow a natural extension of classical genera to these bordism cohomology rings taking values in singular cohomology.
Model for assembly map of bordism-invariant functors.
We consider a category whose morphisms are bordisms of -dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the product of copies of infinite symmetric group. We show that unitary representations of produce functors from the category of …
We discuss an universal bordism invariant obtained from the Atiyah-Patodi-Singer eta-invariant from the analytic and homotopy theoretic point of view. Classical invariants like the Adams e-invariant, -invariants and -bordism invariants are derived as special cases. The main results are a secondary index theo…
PLS-Lasso integrates dimension reduction into regression for financial index tracking.
For every abelian compact Lie group A, we prove that the homotopical A-equivariant complex bordism ring, introduced by tom Dieck (1970), is isomorphic to the A-equivariant Lazard ring, introduced by Cole-Greenlees-Kriz (2000). This settles a conjecture of Greenlees. We also show an analog for homotopical real bordism r…
The book develops a new bordism-theoretic approach to understanding orientations of moduli spaces.
Constructs differential models for twisted Spin^c-bordism and its dual, defining a new anomaly map.
We give a simple sufficient condition for Quinn's "bordism-type spectra" to be weakly equivalent to strictly associative ring spectra. We also show that Poincare bordism and symmetric L-theory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements involves showing that Quinn's funct…
By results of Loeffler and Comezana, the Pontrjagin-Thom map from geometric G-equivariant bordism to homotopy theoretic equivariant bordism is injective for compact abelian G. If G = S^1 x ... x S^1, we prove that the associated fixed point square is a pull back square, thus confirming a recent conjecture of D. Sinha. …
We prove a folklore result which gives a sequence of necessary and sufficient conditions for a stably symplectic manifold to define a nilpotent element in the symplectic bordism ring.
The Bryant-Ferry-Mio-Weinberger surgery exact sequence for high-dimensional compact ANR homology manifolds is used to obtain transversality, splitting and bordism results for homology manifolds, generalizing previous work of Johnston.
Invariants for colored links found, with topological protection of certain knots.
Proves PL cobordism category's homotopy type, analogous to smooth case.
We introduce an equivariant Pontrjagin-Thom construction which identifies equivariant cohomotopy classes with certain fixed point bordism classes. This provides a concrete geometric model for equivariant cohomotopy which works for any compact Lie group G. In the special case when G is finite or a torus, we show that ou…
Paper establishes equivalence between algebraic and functorial QFTs.
Study shows groups can act on torus without extending to 3-manifold.
We describe an algorithm to subdivide automatically a given set of PL n-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements are PL-homeomorphic. The algorithm, implemented in the case n=4, succeeds to solve completely the PL-homeomorphism problem among the catalogu…
Paper confirms conjecture for PL foliations of codimension 2.
The goal of this paper is to study the Pontrjagin dual of (reduced) 4-dimensional Spin bordism. That is to say, we consider the functor from the category of topological spaces to the category of compact abelian groups that associates to each space X the compact group of homomorphisms from the reduced 4-dimensional Spin…
This note corrects an error in the char(K)=2 case of the author's computation of the bordism groups of K-Witt spaces for the field K.
Ricci-positive manifolds span the kernel of the -genus in rational Spin bordism.
In terms of category theory, the Gromov homotopy principle for a set valued functor asserts that the functor can be induced from a homotopy functor. Similarly, we say that the bordism principle for an abelian group valued functor holds if the functor can be induced from a (co)homology functor. We examin…
A modular functor is constructed from non-semisimple 3d TFTs.
Suppose M is a noncompact connected PL 2-manifold. In this paper we study the topological property of the triple (H(M)_0, H^PL(M)_0, H^PL, c(M)_0), where H(M)_0 is the identity component of the homeomorphism group {\cal H}(M) of M with the compact-open topology, and H^PL(M)_0 and H^PL, c(M)_0 are the identity component…
Abstract: Mapping 3-manifold bordisms to topological orders and domain walls.
We give bordism-finiteness results for manifolds with semi-simple group action. Consider the class of oriented manifolds which admit a circle action with isolated fixed points such that the action extends to an -action with fixed point. We exhibit various subclasses, characterized by an upper bound for the Euler c…
Let be a compact Riemannian manifold of positive scalar curvature (psc). It is well-known, due to Schoen-Yau, that any closed stable minimal hypersurface of also admits a psc-metric. We establish an analogous result for stable minimal hypersurfaces with free boundary. Furthermore, we combine this result wit…
A classical theorem due to Quillen (1969) identifies the unitary bordism ring with the Lazard ring, which classifies the universal one-dimensional commutative formal group law. We prove an equivariant generalization of this result by identifying the homotopy theoretic -equivariant unitary bordism ring, in…
High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framewo…
Finite type invariants separate PL links in 3D space.
Paper proves orientability of gauge theory moduli spaces using bordism theory.
We construct a new family of toric manifolds generating the unitary bordism ring. Each manifold in the family is the complex projectivisation of the sum of a line bundle and a trivial bundle over a complex projective space. We also construct a family of special unitary quasitoric manifolds which contains polynomial gen…