NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Initial Amendment Date:	June 26, 1998
Latest Amendment Date:	August 17, 2000
Award Number:	9802480
Award Instrument:	Standard Grant
Program Manager:	Christopher Stark DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	July 1, 1998
End Date:	September 30, 2000 (Estimated)
Total Intended Award Amount:	$63,227.00
Total Awarded Amount to Date:	$63,227.00
Funds Obligated to Date:	FY 1998 = $63,227.00
History of Investigator:	Tomasz Mrowka (Principal Investigator) mrowka@math.mit.edu Matilde Marcolli (Co-Principal Investigator)
Recipient Sponsored Research Office:	Massachusetts Institute of Technology 77 MASSACHUSETTS AVE CAMBRIDGE MA  US  02139-4301 (617)253-1000
Sponsor Congressional District:	07
Primary Place of Performance:	Massachusetts Institute of Technology 77 MASSACHUSETTS AVE CAMBRIDGE MA  US  02139-4301
Primary Place of Performance Congressional District:	07
Unique Entity Identifier (UEI):	E2NYLCDML6V1
Parent UEI:	E2NYLCDML6V1
NSF Program(s):	GEOMETRIC ANALYSIS
Primary Program Source:	app-0198
Program Reference Code(s):	0000, OTHR
Program Element Code(s):	126500
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

Abstract Proposal: DMS 9802480 Principal Investigators: Tomasz Mrowka and Matilde Marcolli The research project consists of three parts. The first goal is the construction of an equivariant version of Seiberg-Witten Floer homology, which is an invariant of the differentiable structure of the underlying three-manifold and avoids the problem of metric dependence that arises in the non-equivariant theory. The second part of the project consists of deriving the exact triangles formulae that detect how the Seiberg-Witten Floer homology changes when the three-manifold is modified by surgery and a suitable cutting and pasting technique that relates the Seiberg-Witten invariants of four-manifolds and three-manifolds. The remaining part of the project is dedicated to the investigation of the relation between the Seiberg-Witten Floer homology and the instanton Floer homology associated to Donaldson theory. The discovery of the Seiberg-Witten invariants, as an outcome of recent developments in string theory, has had a tremendous impact in the field of low dimensional topology. The rich interplay of geometry and theoretical physics has allowed a deeper understanding of the geometric structure of three and four-dimensional manifolds. The topology and geometry of three and four-dimensional manifolds is known to be especially rich of interesting phenomena and open problems: the failure of the classification methods used in higher dimensions makes it particularly important to construct computable invariants, hence the need to investigate the properties of the Seiberg-Witten invariants and their relation to the previously known Yang-Mills-Donaldson theory.

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