Guide Lectures on cobordism theory

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Higher dimensional algebra and topological quantum field theory - Baez, J. Conformal nets and local field theory - Bartels, Arthur et al. Julia E.

Main fields of studies for MISMaP

Four-dimensional topological field theory, Hopf categories, and the canonical bases - Crane, Louis et al. Costello and O. Factorization algebras in perturbative quantum field theory. Kevin Costello, Topological conformal field theories and Calabi-Yau categories.

Cobordism - Wikipedia

Polynomial invariants for smooth manifolds - Donaldson, S. Topology 29 State sums in 2-dimensional fully extended topological field theories, Ph. Douglas, C. Schommer-Pries, and N. The 3-category of tensor categories. A geometrical approach to two-dimensional conformal field theory, Ph. Yakov M. Eliashberg and Nikolai M.

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The space of framed functions is contractible. Higher algebraic structures and quantization - Freed, D. Elementary introduction to quantum field theory, Quantum fields and strings: a course for mathematicians. Deligne et al. Notes by L. AT] AIM Consistent orientation of moduli spaces - Freed, Daniel S.

Chern-Simons theory with finite gauge group - Freed, Daniel S. Batalin-Vilkovisky algebras and two-dimensional topological field theories - Getzler, E. A functional integral point of view. Acta Math. Khovanov-Rozansky homology and topological strings - Gukov, Sergei et al. Rudolf Haag, Local quantum physics, second ed.

Fields, particles, algebras. Kiyoshi Igusa, The space of framed functions. Kirby, A. Robion calculus for framed links in S3.

Lecture 1 - Introduction to Topological Quantum Field Theories - M. Marino - Лекториум

Daniel M. Adjoint functors.

Anton Kapustin, Topological field theory, higher categories, and their applications, Proceedings of the International Congress of Mathematicians. Gromov-Witten classes, quantum cohomology, and enumerative geometry - Kontsevich, M.

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Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. Jacob Lurie, On the classification of topological field theories, Current developments in mathematics, , Int. Press, Somerville, MA, , pp. Jacob Lurie, Higher Algebra draft version. Lectures on the cobordism hypothesis Perspectives in Geometry lectures at University of Texas, January, George W. The mathematical foundations of quantum mechanics: A lecture-note volume, W. Stable algebraic History of topology Amsterdam, , pp. Saunders Mac Lane, Categories for the working mathematician, second ed.

John W. Spivak and R. J Siebenmann and J. Once in a while the list will be updated, extended, or corrected. The basic texts for the definitions of Milnor's K-ring and its norm are [Milnor, ] and [Bass and Tate, ].

The well-definedness of the norm was first proven in [Kato, ]. Sections 1 and 2 of [Rost, ] contain a summary of the basic functorial properties of Milnor's K-theory and other modules over Milnor's K-ring, like Galois cohomology. For symbol algebras cyclic algebras see also [Milnor, ]. The first example of a non-trivial SK 1 is due to [Platonov, ] , see also [Draxl, ] and [Suslin, ]. The non-triviality of the generic element in SK 1 for algebras with index divisible by 4 has been shown in [Merkurjev, ].

Standard references for quadratic forms are [Lam, ] and [Scharlau, ]. For the relations with Milnor's K-theory see [Milnor, ]. For the classical Chow groups see [Fulton, ]. For the groups A p X,n see [Rost, ]. See Corollary The basic references are [Milnor and Stasheff, ] and [Stong, ]. For the Todd numbers and their properties see [Hirzebruch, ]. The denominators of the Todd classes are computed in [Atiyah and Hirzebruch, ]. The Riemann-Roch theorem in the algebro-geometric setting can be found in [Fulton, ].

John W Milnor's books

See [Steenrod, ] , [Milnor, ] , [Margolis, ]. Further references: [Thom, ] , [Ravenel, ] , [Shibata, ] , [Shibata, ] , [Buoncristiano and Hacon, ] , [Buoncristiano and Hacon, ] , [Buoncristiano and Hacon, ] , [Buoncristiano and Hacon, ].

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  • For the formal group law version of the fundamental relation in unoriented cobordism see [Rost, ].