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In this talk, I will introduce the methods for calculating the unstable homotopy groups of finite CW-complexes which builds on works of the relative James construction initiated by B. Gray in 1973 and...
The R-motivic stable homotopy category has a close connection to the C2-equivariant category via the C2-equivariant Betti realization map. For the bigraded homotopy groups, the C2-equivariant spectra...
Chromatic homotopy theory uses the algebraic geometry of smooth 1-parameter formal groups to separate stable homotopy theory into periodic layers. The 1st layer recovers the image of Adams’ J homomorp...
In this talk we study the homotopy type of the (double) suspension of an orientable, closed, connected 4-manifold M, whose integral homology can have 2-torsion. Moreover, the decomposition results are...
his is a relative result which asserts that the K-theory spectra of any two algebraically closed fields of a given characteristic are equivalent to each other after completion at a prime not e...
Traditional structural feedback control systems are centralized systems, whose applications to large scale structures encounter a number of practical difficulties in terms of system reliability, cost,...
This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended ...
Badzioch showed that in the category of simplicial sets each homotopy algebra of a Lawvere theory is weakly equivalent to a strict algebra. In seeking to extend this result to other contexts Rosicky o...
In this paper, we investigate the necessary sufficient conditions for the exactness of the homotopy sequence of Nori's fundamental group and apply these to various special situations to regain some cl...
Abstract: Let p be a fibration over a finite simplicial complex, whose fibers have the homotopy type of finite simplicial complexes. Then p is equivalent to an approximate fibration whose total space ...
Abstract: There are two main approaches to the problem of realizing a $\Pi$-algebra (a graded group $\Lambda$ equipped with an action of the primary homotopy operations) as the homotopy groups of a sp...
Abstract: This is an introductory review of the connection between homotopy theory and path integrals, mainly focus on works done by Schulman [23] that he compared path integral on SO(3) and its unive...
Abstract: We explain how Lie algebroid modules in the sense of Vaintrob provide geometric models for Lie algebroid representations up to homotopy. Specifically, we show that there is a noncanonical wa...
Abstract: This article provides some basic results on weight structures, weight complex functors and homotopy categories. We prove that the full subcategories K(A)^{w < n}, K(A)^{w > n}, K(A)^- and K(...
This paper gives a geometric topological proof that exotic ho-motopy 3-spheres do not exist.

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