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.
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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- The cobordism hypothesis - INSPIRE-HEP.
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, ].