Related papers: Bordism between Dold and Milnor Manifolds
We define four distinct oriented bivariant theories associated with algebraic cobordism in its two versions (the axiomatic $\Omega$ and the geometric $\omega$), when applied to quasi-projective varieties over a field $k$. Specifically, we…
In the first part of this survey we give a modernised exposition of the structure of the special unitary bordism ring, by combining the classical geometric methods of Conner-Floyd, Wall and Stong with the Adams-Novikov spectral sequence and…
A connection is made between the Krammer representation and the Birman-Murakami-Wenzl algebra. Inspired by a dimension argument, a basis is found for a certain irrep of the algebra, and relations which generate the matrices are found.…
We construct a stable infinity category with objects flow categories and morphisms flow bimodules; our construction has many flavors, related to a choice of bordism theory, and we discuss in particular framed bordism and the bordism theory…
The Dold$-$Thom theorem states that for a sufficiently nice topological space, M, there is an isomorphism between the homotopy groups of the infinite symmetric product of M and the homology groups of M itself. The crux of most known proofs…
In view of the Segal construction each category with a coherent operation gives rise to a cohomology theory. Similarly each open stable differential relation $R$ imposed on smooth maps of manifolds determines cohomology theories $k^*$ and…
In this note I give a positive solution to Bullett's conjecture (posed in [1]) regarding a geometric presentation of the universal mod $p$ oriented ring spectrum.
A sort of calculus is developed to find the chiral algebras of N=2 superconformal interacting bosonic models. Many examples are discussed. It is shown that the algebras share a common structure, which we call almost Landau Ginzburg. For one…
We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold bundles. In this context, Haefliger-Thurston's conjecture predicts that every $M$-bundle over a manifold $B$ where $\text{dim}(B)\leq…
For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting…
We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…
We give a full classification of representation types of the subcategories of representations of an $m \times n$ rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions, which appear naturally in the context of…
In this short note we give an explicit presentation of the algebra A_n generated by the curvature 2-forms of the standard Hermitiam line bundles over SL_n/B as the quotient of the polynomial ring. The difference between A_n and H^*(SL_n/B)…
We prove bordism invariance of the coarse index of complex elliptic pseudodifferential operators. In our discussion we introduce directed $c$-bordisms, whose usefulness is illustrated in the context of existence of uniformly positive scalar…
We introduce M\"obius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and M\"obius strip features. We identify the resulting diagram…
In this work we investigate the Swampland Cobordism Conjecture in the context of type IIB string theory geometries with non-trivial duality bundle. Quite remarkably, we find that many non-trivial bordism classes with duality bundles in…
This is the second part of the work on differential models of the Anderson duals to the stable tangential $G$-bordism theories $I\Omega^G$, motivated by classifications of invertible QFT's. Using the model constructed in the first part…
This note concerns Legendrian cobordisms in one-jet spaces of functions, in the sense of Arnol'd \cite{Arnold} -- consisting of big Legendrian submanifolds between two smaller ones. We are interested in such cobordisms which fit with…
We show the $\TT^2$-cobordism group of the category of 4-dimensional quasitoric manifolds is generated by the $\TT^2$-cobordism classes of $\CP^2$. We construct nice oriented $\TT^2$ manifolds with boundary where the boundary is the…
We introduce a spherical variant of Milnor's classifying construction for diffeological groups, based on quadratic normalization of barycentric coordinates. This construction gives rise to a contractible diffeological space endowed with…